text:
'Black snow' from sugarcane harmful to Black, poor communities in Florida?
By J.S. Adams Contributing Writer @niiahadams
Thick black smoke plumes from sugarcane fields near Belle Glade, Fla., a predominantly Black community west of West Palm Beach and just south of Lake Okeechobee. Residents watch as red-orange flames engulf the sugarcane fields as the industry prepares for harvesting season.
These annual burnings, which take place from October to March, May or June, make it easier for farmers to harvest the sugarcane.
'Black snow' or ashes fall on top of vehicle in Glades community. Photos via Stop Sugar Field Burning Now/Facebook
However, the side effects leave the residents of Belle Glade, South Bay and Pahokee with respiratory problems and a poor quality of life.
While these burnings have been going on for several years with groups rising up to combat them, a recent lawsuit against the Florida sugar industry has brought it to national light, bringing attention to an issue that has forced residents to take a stand.
The lawsuit, filed by the Berman Law Group in June, seeks to permanently end the pre-harvesting burning, obtain economic and property damages, and health monitoring, particularly for children, the poor and elderly.
Horses graze in a field near the U.S. Sugar Corporation's mill and refinery in Clewiston, Fla. Nov. 8, 2001. Photo: AP Photo/Amy E. Conn
"The firm has been working on this issue for a long time prior to me joining," said Joseph Abruzzo, director of government relations for the Berman Law Group. "What put them on track was several clients alerting them to what was occurring with them and that spawned the investigation into hiring the experts (and) finding what was in the air of the Glades community."
Joining the fight in this lawsuit is Frank Biden, the younger brother of Presidential candidate Joe Biden, and former NFL player Fred Taylor, who grew up in the Glades community. In a video produced by the Berman Law Group, both agree the burnings need to stop.
The sugar industry burns about nine million tons of sugarcane foliage on 400,000 acres each year. EarthJustice, a legal group for environmental organizations, says the burning puts out more than 2,800 tons of hazardous pollutants into the air annually. According to the Sierra Club, an environmental non-profit organization, the sugarcane is burned in order to rid the plant of its outer layer so that the sugar stalk will remain.
Patrick Ferguson, the organizing representative for the Sierra Club's Stop Sugar Field Burning Campaign, said health issues due to the burnings are a major concern.
"Exposure to pre-harvest sugar field burning pollution has been linked via medical research to many negative health impacts including respiratory diseases, cancer, cardiac disease, and poor infant health outcomes," he said. "Many of the campaign volunteers either themselves suffer from respiratory issues or have family members who do. Some of our volunteers have young children who have to use breathing devices during the 6-8 months long harvesting season when sugarcane is burned."
The lawsuit alleges that due to the burning, harmful pollutants are released into the air. It creates "black snow" during burn season, or ashes that fall down onto the Glades communities. Because of this, children in the Glades communities use breathing machines at night and walk to school with trash bags over their head to protect them from the black snow.
"There's a lake, they have issues," Mr. Abruzzo said. "I wasn't too long ago out at one of the churches and multiple ladies had on white dresses. They know when the ash falls on your dresses ... . You can't swipe it away because it will create a black line. You blow it. The black snow is right in front of their faces, on their car, over their homes and worst of all, it's in the lungs of the children and elderly."
The Poor People's Campaign held an event in Belle Glade where residents, pastors and activists had the chance to share their experiences about the burnings.
Steve Messam
Steve Messam, a pastor born and raised in Belle Glade, shared how his father came to the United States from Jamaica as a contracted migrant worker hired to cut the sugarcane. The pastor got involved with the Sierra Club's campaign because he noticed many of the people he knew were suffering from breathing difficulties.
"They were suffering from a lot of respiratory issues, whether it was asthma or allergies," he said during Poor People's Campaign gathering. "A lot of people were also dying from cancer at a crazy rate."
Mr. Ferguson says the black snow and air quality affects not only health issues, but the community's quality of life.
"You're talking about the harvesting season lasting from October to May, some of the best months to be outside and enjoy the Florida weather and during days when large amounts of toxic burning takes place, people in the region are often forced to stay indoors," he said.
Alina Alonso, director of the Florida Department of Health in Palm Beach County, said the health department uses a website called airnow.gov to monitor air quality within the region. She said air quality counts remnants that come from ash and into the air. The website measures air quality ranging from good to hazardous.
"Only those who are sensitive to the smoke or burnings will be affected by moderate," Ms. Alonso said. "But if it gets above 100, then that's unhealthy for everyone."
Mr. Ferguson said many doctors in the area suggest options for residents that aren't always reasonable.
Pre-harvest sugar burning in the Glades. Photos via Stop Sugar Field Burning Now/Facebook
"One common thread that we continue to hear is that doctors tell residents from the communities heavily impacted by pre-harvest sugar field burning that the best long term solution for their health issues is to move to an area with better air quality, which many residents don't have the resources or the will to do so, nor should they have to do so," he said.
Back in 2015, the Sierra Club filed a legal action asking the U.S. Environmental Protection Agency to regulate the burnings.
"The way sugarcane burning is regulated makes it an environmental justice issue as well. Regulations in place are based off wind speed and direction that prevent burn permits from being issued when the winds would carry the smoke and ash toward the more affluent in eastern Palm Beach County," Mr. Ferguson said. "However minimal protections are in place from the toxic smoke and ash when they blow toward the lower income rural communities within the Everglades Agricultural Area. This leads the predominantly African-American and Hispanic population of the Glades communities of western Palm Beach County that are surrounded by over 75 percent of the total sugarcane acreage in Florida to disproportionately bear the negative impacts of pre-harvest sugar field burning."
The alternative that's offered to the sugarcane industry is green harvesting.
"The Florida sugarcane industry already green harvests in small amounts each year. Other countries around the world have been phasing out of burning altogether because of the negative health and environmental impacts of pre-harvest burning but also because of the many benefits associated with green harvesting as well," Mr. Ferguson said.
Because of the pre-harvest burning, the Glades communities have suffered economically as well. Mr. Abruzzo said whereas Palm Beach county and the state of Florida have seen an increase in real estate values, property values for the Glades community remain stagnant.
"Everybody knows if you move out there, you'll have to deal with four months of black snow over your home," Mr. Abruzzo said.
Mr. Ferguson believes that a shift towards green harvesting can help improve the economic condition of the community.
"[It] can create more economic opportunities which are important especially for the lower income Glades communities," he said. "What the sugar industry considers as trash can be used to generate more electricity, create mulch, biochar, biofuels, and can even be used to create tree-free paper products."
Florida sugar companies have caught wind of the Berman Group's lawsuit and say that they believe in their practices.
"The health, safety and jobs of our communities all are vitally important to U.S. Sugar," spokeswoman Judy Sanchez told Treasure Coast Newspapers in a statement. "We are American farmers and stand behind the safety and integrity of our farming practices, which are highly regulated and legally permitted on a daily basis by the government. Our farming practices are safe, environmentally sound, highly regulated and closely monitored."
Ms. Sanchez also said company officials "live in these Glades communities and raise our families here—our children and grandchildren—in the neighborhoods, schools and churches throughout these small, close-knit farming towns."
Mr. Abruzzo said he's looking forward to the company providing the names of those officials who live in the area.
"One of the most disappointing things since the lawsuit was filed is the propaganda that the sugar companies are helping lead that we are well aware of and without question will be discussing in depositions, primarily, that the lawsuits are trying to put sugar out of business. That could be anything but the truth," he said. "The sugar companies profit in the billions of dollars per year. I'm sure they wouldn't even notice on their balance sheets doing it a proper way and not harming an entire community. This would create more jobs if they do it by hand. At the end of the day, they just can't burn."
Mr. Ferguson and volunteers that work with him have spent the past four years pressing this issue. He said it's something that must be known all around the country.
"There's no reason the sugarcane industry should continue to put short term profits ahead of the long-term health and welfare of the surrounding residents, especially when there are so many benefits that can be gained from transitioning to green harvesting," he said. "It's time for the industry to become better neighbors to the surrounding communities by stopping the burn and switching to green harvesting."
"I believe it's a very good thing that attention is being paid to this very important issue. The Glades has been suffering for a very long time." Mr. Abruzzo said. "Ultimately, I do believe that the law will be with the people. Once this is corrected, I believe the Glades will stop being one of the poorest places in the country. It will be vibrant and flourishing."
Mr. Abruzzo said the first step after the legal filing is to immediately get the sugar industry to stop burning while the case is going on. This case is federal, but they also plan to file state and individual claims.
Posted by Muhammad's Study Group of Grand Rapids, Michigan at 3:00 AM


Additional Notes: Congrats to Actress/Social Media Influencer Mahogany LOX on booking and airing the role of Suitcase Model #13 airing December 5, 2018 with Howie Mandel as the host. Mahogany has over 5 million followers collectively. @MahoganyLOX! She's HOT!!!


To help first-year students prepare for MATH courses at the 2000 level.
To enhance an atmosphere that promotes the discussion of mathematics within the Department.
A test will be held on May 10, 2019 (Friday) from 3:00pm-5:00pm at LSB C1, for eligible and registered first-year MATH students (see point 4 below).
To assist in the preparation for the aforementioned test, and to foster an atmosphere for discussion of mathematics, some senior MATH students will run the First-Year Honours Class.
Term 2 - Jan 14, 21, 28, Feb 11, 18, 25, Mar 4, 11, 18, 25, Apr 8, 15.
All classes are to be held on Monday night from 6:30pm-8:15pm at LSB C1 (tentatively).
This will be a unique learning opportunity where students will be guided to solve some interesting mathematics problems. Students are encouraged to come to this class regularly to practice your mathematical skills.
*A student will at least obtain a pass if he/she attends at least 80% of the First-Year Honours Class. Any higher honour has to be attained by a satisfactory performance on the test.
The test will cover the content of MATH 1010, 1030, 1050, plus anything that might appear in past HKALE Pure Mathematics examinations (starting from 1994).
CUHK Library. (`UL Gov Document' on the 1/F of the University Library, 'CC Gov Document' on the LG/F of the Chung Chi Library).
Here are some sample questions, and here is the question paper of year 2016, 2017 and 2018.
A student is eligible for the First-year honours scheme if he/she is admitted to The Chinese University of Hong Kong in 2018, and have become a MATH major by August 31, 2019. Interested eligible students should register in the form below (end of page) in order to participate in the scheme.
Q: Is this compulsory for first-year MATH students?
A: No, this is entirely voluntary, but the scheme is designed to help first-year MATH majors build a more solid foundation. We hope this will help them succeed in MATH courses at 2000 level (and beyond), so we encourage *all* first-year MATH majors to participate.
Q: Why do we need to take one more test on top of the final examinations of the first year MATH courses?
A: The first year MATH curriculum is constrained by the teaching hours available. Many useful techniques, that used to be covered in HKALE Pure Mathematics examinations, are not treated to sufficient depth in the first-year MATH courses. In particular, experience shows that being able to do well in the final examinations of first-year MATH courses does not necessarily guarantee a solid preparation for second-year MATH courses. This is partly why we come up with this honours scheme, as a supplementary means to bridge this gap between the first and second years.
Q: How hard is the test going to be?
A: It is going to be harder than the final exams of MATH 1010, 1030, 1050 and HKDSE. It will be more akin to the level of difficulty of past HKALE Pure Mathematics examinations.
Q: Is there any 'punishment' for not doing well in the test?
A: No, absolutely not. In the worst case a student recognizes that he/she may need to catch up a bit, and we are always here to help. We take it as a good sign if a student is willing to put in effort.
Q: Is this program for students in the MATH enrichment program only?
A: No. You can participate as long as you were admitted to CUHK in 2017, and have become a MATH major by August 31, 2018. For instance, we expect many of you to be first-year MATH majors admitted through the Broad-Base Science Program.
Q: Is this program aimed at 'top students' only?
A: No, even though this program is called an 'honours scheme', we expect most (if not all) first-year MATH majors to participate. We hope that regardless of your mathematical background, you will all learn something through participation in this scheme.
Q: If I feel very prepared for the second-year MATH courses already, should I still participate in this scheme?
A: We still encourage you to take part in the scheme. After all, there is no harm getting an honour. We will try to make it fun to take part in the test, and we hope all of you will learn something from the questions we set.
Q: How should I prepare for this test?
A: We suggest that you take this chance to review all the material you have learned in MATH 1010, 1030, 1050, and also attempt as many questions as you could in the past HKALE Pure Mathematics examination papers. It should help too if you come regularly to the honours class, that is held every Monday starting from week 2 of each semester.
Were you admitted to CUHK in 2018?


In April 2017, our Dealer Principal Nathan Hayes joined the Pollie Pedal ride in support of Soldier on. Gerald Slaven Holden & Volkswagen are incredibly proud to partner with an organisation we hold in high regard for their commitment to supporting our returning service men and women.
Our partnership with the organisation is just another way we can give back to the community that supports our dealership.
We trust our sponsorship will assist Soldier On in continuing their amazing work.
The Convoy for Cancer is part of the fundraising efforts of the Cancer Support Group and is held every year in Canberra where hundreds of trucks and Bikes form a convoy Kilometres long with the shared goal of raising much needed funds for Cancer research.
2018 saw as many as 430 Trucks and 250 Bikes take part in the Huge event which starts in Queanbeyan and ends in Exhibition Park in Canberra. Here all participants embark of an afternoon of relaxing, listening to good music and catching up with their friends they've met throughout the years.
It was yet again a big honour to be a part of this amazing event. A great day was had by everyone and the money rasied will help a fantastic cause.
Kids with Cancer Foundation are a true Not for Profit Organisation raising funds to find a cure for childhood cancer. All funds raised go directly towards research, childrens hospitals and the families affected by Childrens Cancer. They are the largest single donator to the Childrens Hospitals and have managed to raise well over $17 Million Dollars so far.
Gerald Slaven is proud to support numerous initiatives with this Organisation and will continue to support their efforts to cure childhood cancer.
We are proud supporters of and contributors to the HSV and HDT owners club of ACT. We hold an annual show and shine for the club each November here at our Holden / HSV showroom. To keep and eye out for the next event please visit our main supporters page here.


Just Listed one acre of land on 3RD AVENUE located in in the "sun belt" of Hawaiian Paradise Park subdivision.
Build your dream home on the big island of Hawaii.
Lot 2716 Estimated dimensions 135 x 322.67.
Great find with very few trees and currently no neighboring homes on either side of the subject lot or across the street.
Subject parcel is kiddy corner from a 20 acre parcel located across the road.
Check it out today before it's sold!
Directions:Highway 130 take Kaloli Drive go toward the ocean, turn right on 3rd Avenue, it's the 11th lot on your left side, sign posted.


1354 Coral Park Lane 603 is a $275,000, 3 bedroom, 3.0 bath home located in Vero Beach, FL.
Steps to the Beach Sits a Charming & Spacious 3 BR, 2&1/2 BA condo w/a 1 car garage waiting for you! Natural Light Fills every Room thru windows of various geometric shapes, Vaulted Ceiling in the BR's add flare. A fire place to cozy up to for a rare Florida Chill, Enjoy a East facing Screened Lanai All year, Formal living rm, dining rm, Breakfast nook for entertaining, Amenities Galore!
I am interested in 1354 Coral Park Lane 603, Vero Beach, FL 32963.


text:
Special Issue: Re-examining Asia-Pacific War Memories: Grief, Narratives, and Memorials (Table of Contents)
Edited by Justin Aukema, Daniel Milne, Mahon Murphy, and Ryota Nishino
Volume 20 | Issue 10
Article ID 5696
This special issue introduces thirteen original essays, each offering unique perspectives and re-examinations of Asia-Pacific War memories. The special issue's broad geographical scope stretches the Asia-Pacific region. Essays' diverse topics and themes highlight previously unexplored avenues and voices, from war cemeteries in Malaysia, to Japanese veterans' complicated war narratives, and to war brides in New Zealand. Each explores a different facet of how war memories shaped and navigated a shifting postwar terrain and complex geopolitics. Toward this end, the special issue is woven around three broad themes in particular: sites of mourning, personal narratives, and commemoration and memorialization.
1. Justin Aukema, Daniel Milne, Mahon Murphy, and Ryōta Nishino - Re-examining Asia-Pacific War Memories: Grief, Narratives, and Memorials
Part I Sites of Mourning
2. Collin Rusneac - Building Transnational Memories at Japanese War and Colonial Cemeteries
3. Alison Starr - Forever Alongside: War Cemeteries as Sites of Enemy Reconciliation
4. Beatrice Trefalt - Finding the remains of the dead: photographs from a Japanese mission to New Guinea, 1969-1970
Part II Personal Narratives
5. Justin Aukema - A Hero's Defeat: Modernization Theory and Japanese Veterans' Asia-Pacific "War Tales"
6. Ryōta Nishino - War, Trauma, and Humanity in a Japanese Veteran's New Guinea War Memoir: Ogawa Masatsugu's "Island of Death" (1969)
7. Matthew Allen - Robots, Kamikaze and War Memory: How a Children's Comic can Help us Rethink Postmemory in Postwar Japan
Part III Commemoration and Memorialization
8. Elena Kolesova and Mutsumi Kanazawa - Ambivalence of Identity: Stories of the Japanese War Brides in New Zealand
9. Daniel Milne and David Moreton - Remembering and Forgetting the War Dead at Ryōzen Kannon: A Site of Entangled and Transnational War Memories
10. Arnel Joven - Remembering Camp O'Donnell: From Shared Memories to Public History in the Philippines
11. Mo Tian - The Legacy of the Second Sino-Japanese War in the People's Republic of China: Mapping the Official Discourses of Memory
12. Mahon Murphy - Entangled Memories of Two World Wars
This is the Table of Contents for The Special Issue: Re-examining Asia-Pacific War Memories: Grief, Narratives, and Memorials, edited by Justin Aukema, Daniel Milne, Mahon Murphy, and Ryota Nishino.
Introduction, Part I and II will be published on May 15, 2022.
Part III and Concluson will be published on June 1, 2022.
Justin Aukema is an Associate Professor in the Faculty of Economics at Osaka Metropolitan University. He received his Ph.D. from Sophia University in 2020. Aukema has written broadly on topics of war history and memory in Japan. Some of his previous articles include "The Need to Narrate the Tokyo Air Raids: The Literature of Saotome Katsumoto" in The Routledge Handbook of Modern Japanese Literature (2016) and "Cultures of (Dis)remembrance and the Effects of Discourse at the Hiyoshidai Tunnels," Japan Review, No.32 (2019). He can be contacted at aukemajk@gmail.com
Daniel Milne is Senior Lecturer at Kyoto University's Institute for Liberals Arts and Sciences (ILAS). His research focuses on the modern history of tourism in Japan and Kyoto, and the political and cultural role the discourses and spaces of tourism have played in war, occupation, and reconciliation. In 2019, Daniel co-edited "War, Tourism, and Modern Japan," a special issue of Japan Review. His current research is supported by a JSPS Grant-in-Aid for Scientific Research on POW tourism and reconciliation.
Ryōta Nishino is Designated Assistant Professor at the School of Law, Nagoya University, Japan. His research interests revolve around the circulation of history and historical memory in various media such as school textbooks and travelogues (Studies in Travel Writing, Japanese Studies, Journal of Pacific History, and Pacific Historical Review). His second book, Japanese Perception of Papua New Guinea: War, Memory and Travel, is due in October 2022 from Bloomsbury Academic.
Mahon Murphy is an Associate Professor at the Faculty of Law, Kyoto University. His research interests focus on the First World War as global war, internment, and the interaction of empires during warfare. He is the author of Colonial Captivity During the First World War: Internment and the Fall of the German Empire, 1914-1919 Cambridge University Press, 2017.
Mouse over to see security code
Speak It

redpajama_set_name: RedPajamaCommonCrawl


text:
\section{Introduction and Statement of Result}\label{introduction}
It is a famous conjecture there are infinitely many primes of the form $n^2 + 1.$ This seemingly innocuous question has a long history and is the motivation for many deep results. Following this problem, one can see that any prime of the form $n^2 + 1$ is also of the form $a^2 + b^2$, and may ask the more general question of how many primes are there of this form, with $a$ small in comparison to $\sqrt{p}$.  In answer to this, Kubilius proved in 1952 that there are infinitely many primes $p$ of the form $p = a^2 + b^2,$ where $a = O(p^{25/64})$, a result that has been improved several times since. The best result of this form to date, due to Harman and Lewis \cite{H-L}, states that there are infinitely many primes $p = a^2 + b^2$ with $a = O(p^\theta)$, for $\theta < 0.119.$

We proceed along a different route.  We observe that $p\geq 3$ is prime, then there exist $a,b\in{\mathbb Z}$ such that $p=a^2+b^2$ if and only if $p\equiv 1\pmod{4}$.  The representation of $p$ as $a^2+b^2$ is unique provided that $a$ is odd, $a+b\equiv 1\pmod{4}$, and $b>0$.  This representation is closely related to the elliptic curve over ${\mathbb Q}$ defined by
\[
E:y^2=x^3-x,
\]
which is closely tied to the ``congruent number problem'' of classifying the integers $n\geq 1$ that are the areas of triangles with rational side lengths.  If $p=a^2+b^2$ with $a$ and $b$ chosen as above, then $p+1-\#E(\mathbb{F}_p)=2a$, where $\mathbb{F}_p$ is the finite field of $p$ elements and $E(\mathbb{F}_p)$ is the group of ${\mathbb F}_p$-points on the modulo $p$ reduction of $E$.  By modularity, there exists a holomorphic cusp form $f_E(z)$ of weight $2$ and level $32$ such that
\[
f_E(z) = \sum_{n=1}^{\infty}a_E(n)e^{2\pi i n z},
\]
where $a_E(p)=p+1-\#E({\mathbb F}_p)$ for primes $p\geq 3$, and the number $a_E(n)$ at an integer $n\geq 2$ is generated from $a_E(p)$ by multiplicativity.  Moreover, the function $f_E(z)$ is an eigenfunction of all of the Hecke operators, and $a_E(1)=1$.  Finally, we can express $f_E(z)$ explicitly as an $\eta$-quotient, namely
\[
f_E(z) = \eta(4z)^2\eta(8z)^2
\]
It is important to note that the primes $p\equiv 3\pmod{4}$ are precisely the primes which are inert in ${\mathbb Q}(i)$.  By the prime number theorem for arithmetic progressions, the asymptotic density of such primes is $1/2$.  In Section 2, we will define the $\eta$-quotient and use its combinatorial properties to prove the above claim on the relationship between $p+1-\#E(\mathbb{F}_p)$ and primes of the form $p=a^2+b^2$.

More generally, let
\[
E:y^2 = x^3+ax^2+bx+c
\]
be an elliptic curve over ${\mathbb Q}$ of conductor $N$ that has complex multiplication by an imaginary quadratic field $K$.  Such a field $K$ necessarily has class number 1, so all integral ideals are principally generated and all elements of $K$ have a unique factorization into prime elements of $K$.  Define $a_E(p) = p+1-\#E({\mathbb F}_p)$.  If $p$ is inert in $K$, then $a_E(p)=0$.  It follows from work of Hasse that if $p$ is prime, then $|a_E(p)| < 2\sqrt{p}$.  Hence we can define $\theta_p \in [0, \pi]$ as the solution to
\[
a_E(p) = 2\sqrt{p}\cos\theta_p.
\]
Now, we ask the natural question of how the sequence ${\theta_p}$ is distributed in the interval $[0, \pi]$.  The answer follows from work of Hecke \cite{hecke}

\begin{theorem*}
Let $E/{\mathbb Q}$ be an elliptic curve of conductor $N$ that has complex multiplication by an imaginary quadratic field.  For a prime $p$, define $\theta_p \in [0, \pi]$ by the equality
\[
p+1-\#E({\mathbb F}_p) = 2\sqrt{p}\cos{\theta_p}.
\]
If $I \subseteq [0, \pi]$ is an open subinterval, then
\begin{equation}
\label{eqn:ST_CM}
\lim_{x \to \infty} \frac{\#\{ p \le x : \theta_p \in I\}}{\#\{p\leq x\}} = \frac{\mathbf{1}_{\frac{\pi}{2}\in I}}{2}+\frac{|I|}{2\pi},\qquad\text{where}\qquad \mathbf{1}_{\frac{\pi}{2}\in I}=\begin{cases}
	1&\mbox{if $\frac{\pi}{2}\in I$,}\\
	0&\mbox{otherwise.}
\end{cases}
\end{equation}
\end{theorem*}

Here, we prove a result that contains several refinements of Hecke's work.  First, rather than merely achieving an asymptotic distribution, our result provides a variant of \eqref{eqn:ST_CM} which also explicates the rate of convergence in the limit.  Second, our result provides strong uniformity in the length of the interval $I$ in which the angles $\theta_p$ lie, enabling us to look at the small-scale distribution of the angles $\theta_p$ as well as the large-scale distribution.  Finally, our result provides strong uniformity in the length of the interval in which the primes themselves lie, enabling us to look at both the small-scale and large-scale distribution of the primes $p\in[x,x+h]$ satisfying $\theta_p\in I$.

\begin{comment}
Let $K = {\mathbb Q}(\sqrt{-n})$ have ${\mathcal O}_K$ as its ring of integers, and
\[
D = \begin{cases} -n & n \equiv 3 \pmod{4} \\ -4n & n \equiv 1, 2\pmod4 \end{cases}
\]
denote the discriminant of $K$ over ${\mathbb Q}.$
For an integral ideal ${\mathfrak a},$ $\Lambda({\mathfrak a})$ is the generalized von Mangoldt function
\[
\Lambda({\mathfrak a}) = \begin{cases} \log{N({\mathfrak p})} & {\mathfrak a} = {\mathfrak p}^{j} \text{ for some prime ideal } {\mathfrak p} \\ 0 & \text{ otherwise }\end{cases}
\]
where $N$ is the absolute norm of an ideal. For each principal ideal ${\mathfrak a} = (a + b\sqrt{-n}),$ define $\arg{{\mathfrak a}} = \arg(a + b\sqrt{-n}).$
Define $g$ as the number of units of $K$.
Let $\chi \xi_{m}$ be the Hecke Grossencharacter defined on principal ideals $(\alpha)$ as
\[
\xi_{m}((\alpha)) = \Big( \frac{\alpha}{|\alpha|} \Big)^{mg}
\]
where $\chi$ is a ray class character.
We have the following prime counting function
\[
\pi_{I, \delta}([x, x+h]) \coloneqq \sum_{\substack{x < p \le x+h \\ \theta_p \in I}}1.
\]
Per usual, we instead study its log counterpart
\[
\sum_{\substack{x < p \le x+h \\ \theta_p \in I}}\log{p} \coloneqq \sum_{\substack{x < p \le x+h \\ \theta_p \in I}}\log{p}.
\]
\end{comment}
\begin{theorem}
\label{thm:main_theorem}
Let $E/{\mathbb Q}$ be an elliptic curve of conductor $N$ that has complex multiplication by an imaginary quadratic field.  Let $I \subseteq [0, \pi]$ be a subinterval, and define $\theta_p \in [0, \pi]$ by
\[
p+1-\#E({\mathbb F}_p) = 2\sqrt{p}\cos{\theta_p}.
\]
Let $\delta>0$ and $\delta'>0$ be fixed numbers such that $\delta+\delta'<\frac{5}{24}$, $h\geq x^{1-\delta}$, and $|I|\geq x^{-\delta'}$.  There exists a number $c=c_{\delta,\delta',E}>0$ such that
\[
\sum_{\substack{x < p \le x+h \\ \theta_p \in I}}\log{p} = \Big(\frac{1}{2}\mathbf{1}_{\frac{\pi}{2}\in I}+\frac{|I|}{2\pi}\Big)h\Big(1 + O\Big(\exp\Big(-c\frac{(\log x)^{1/3}}{(\log\log x)^{1/3}}\Big)\Big).
\]
The implied constant depends on $N$.
\end{theorem}

In Section 2, we present some explicit examples of the relationship between the numbers $a_E(p)$ for elliptic curves $E/\mathbb{Q}$ with complex multiplication and primes represented by certain positive-definite binary quadratic forms.  This relationship uses the Jacobi triple product formula and gives rise to the claimed connection between primes of the form $a^2+b^2$ and the elliptic curve $y^2=x^3-x$.  One can recast Theorem \ref{thm:main_theorem} as a statement about the distribution of primes represented by these quadratic forms.  In this context, Theorem \ref{thm:main_theorem} reproves a result of Coleman \cite{coleman1990}.  For related work on more general norm forms, see Duke \cite{duke}.

After we prove Theorem \ref{thm:main_theorem}, we describe how one can extend our results to a much broader context.  In particular, our ideas extend to study the distribution of Fourier coefficients of holomorphic cuspidal Hecke eigenforms which are also CM newforms.  We will indicate how Theorem 1.1 fits into this context, which can be addressed using class field theory.

\subsection*{Acknowledgements} This research was supported by the NSF (DMS-2002265), the NSA (H98230-20-1-0012), the Templeton World Charity Foundation, and the Thomas Jefferson Fund at the University of Virginia. The authors would like to thank Dr. Ken Ono for his many helpful suggestions and conversations.

\section{Combinatorial properties of newforms}

In this section, we first discuss the combinatorial properties of the Dedekind eta-function, defined by the infinite product
\[
\eta(z) \coloneqq q^{1/24}\prod_{n=1}^{\infty}(1 - q^n),
\]
where $q = e^{2\pi iz}$. We include this note to give insight into how the binary quadratic forms that we represent primes by arise. Using this function, we can easily provide explicit descriptions of many modular forms. It is also useful for producing generating functions. To do this, we make use of Jacobi's Triple Product Identity
\[
\label{jacobiidentity}
\prod_{n=1}^{\infty}(1 - x^{2n})(1+x^{2n -1}z^2)(1+x^{2n-1}z^{-2}) = \sum_{m \in {\mathbb Z}}z^{2m}x^{m^2}.
\]
Thus, we have the following identities.
\begin{proposition}
The following q-series identities are true.
\label{identities}
\begin{align*}
    \eta(24z) &= q\prod_{n=1}^{\infty}(1 - q^{24n}) = \sum_{k \in {\mathbb Z}}(-1)^kq^{(6k+1)^2} \\
    \frac{\eta(z)^2}{\eta(2z)} &= \prod_{n = 1}^{\infty} \frac{(1 - q^n)^2}{(1 - q^{2n})} = \sum_{k \in {\mathbb Z}}(-1)^kq^{k^2} \\
    \eta(8z)^3 &= q\prod_{n=1}^{\infty}(1 - q^{8n})^3 = \sum_{k =0}^{\infty}(-1)^k(2k + 1)q^{(2k+1)^2} \\
    \frac{\eta(6z)^5}{\eta(3z)^2} &= q\prod_{n=1}^\infty \frac{(1 - q^{6n})^5}{(1 - q^{3n})^2} = \sum_{n=1}^{\infty}(-1)^{n-1}\Big(\frac{n}{3}\Big)nq^{n^2} \\
    \frac{\eta(2z)^5}{\eta(z)^2 \eta(4z)^2} &= \prod_{n=1}^\infty \frac{(1 - q^{2n})^5}{(1 - q^n)^2(1-q^{4n})^2} = \sum_{k \in {\mathbb Z}}q^{k^2}

\end{align*}
\end{proposition}
\begin{proof}
See \cite[Section 1.4]{ono-cbms}.
\end{proof}
Consider the functions
\begin{equation}
\label{eqn:newform_examples}
\begin{aligned}
    f_{E_1}(z) &= \eta(4z)^2\eta(8z)^2 = \sum_{n=1}^{\infty} a_{E_1}(n)q^n, \\
    f_{E_2}(z) &= \eta(6z)^4 = \sum_{n=1}^{\infty} a_{E_2}(n)q^n, \\
    f_{E_3}(z) &= \frac{\eta(8z)^8}{\eta(4z)^2\eta(16z)^2} = \sum_{n=1}^{\infty} a_{E_3}(n)q^n.
\end{aligned}
\end{equation}
From \cite{martin-ono}, the corresponding elliptic curves for these weight 2 newforms are
\begin{align*}
    E_{1} &: y^2 = x^3 - x ,\\
    E_{2} &: y^2 = x^3 + 1 ,\\
    E_{3} &: y^2 = x^3 - 4x.
\end{align*}
The curve $E_2$ with conductor 36 has complex multiplication by $\mathbb{Q}(\sqrt{-3}),$ and the curves $E_1$ and $E_3$ with conductor 32 and 64, respectively, have complex multiplication by ${\mathbb Q}(i)$. This implies that $L(s,E_{j}),$ for $j \in \{1, 2, 3\}$ is a Hecke L-function $L(s, \phi)$, for a suitable Hecke Gr\"ossencharacter $\phi$. Since the curves $E_{j}$ have complex multiplication, we can find the explicit formulae for the coefficients for $L(s, \phi)$ using the well-known $q$-series identities seen in Corollary \ref{identities}. We use this to compute the Fourier coefficients of the weight 2 newforms from above, which are sums of the relevant Hecke Gr{\"o}ssencharacters.
\par
Using the $q$-series and infinite product identities in Proposition 2.1, we see that
\begin{align*}
    \eta(4z)^2\eta(8z)^2 &= \frac{\eta(4z)^2}{\eta(8z)}\cdot \eta(8z)^3 = q\prod_{n=1}^{\infty}(1 - q^{8n})^3 \cdot  \prod_{m = 1}^{\infty} \frac{(1 - q^{4m})^2}{(1 - q^{8m})} \\
    &= \Big(\sum_{n =0}^{\infty}(-1)^n(2n + 1)q^{(2n+1)^2} \Big) \cdot \Big(1 + 2\sum_{m=1}^\infty (-1)^{m}q^{4m^2}\Big), \\
    \eta(6z)^4 &= \frac{\eta(6z)^5}{\eta(3z)^2} \cdot   \frac{\eta(3z)^2}{\eta(6z)} =
    q\prod_{n=1}^{\infty} \frac{(1 - q^{6n})^5}{(1 - q^{3n})^2} \cdot \prod_{m=1}^{\infty} \frac{(1 - q^{3m})^2}{(1 - q^{6m})} \\
    &= \Big(\sum_{n=1}^\infty (-1)^{n-1}\Big(\frac{n}{3} \Big) nq^{n^2}\Big) \cdot \Big(1 + 2\sum_{m=1}^\infty (-1)^{3m}q^{3m^2} \Big),\\
    \frac{\eta(8z)^8}{\eta(4z)^2\eta(16z)^2} &= \eta(8z)^3 \cdot    \frac{\eta(8z)^5}{\eta(4z)^2\eta(16z)^2} = q\prod_{n=1}^{\infty}(1 - q^{8n})^3 \cdot \prod_{n=1}^\infty \frac{(1 - q^{8n})^5}{(1 - q^{4n})^2(1-q^{16n})^2} \\
    &= \Big(\sum_{n =0}^{\infty}(-1)^n(2n + 1)q^{(2n+1)^2}\Big) \cdot \Big(1 + 2\sum_{m=1}^\infty q^{4m^2}\Big).
\end{align*}
Since the coefficients are Hecke multiplicative, it suffices to give the formulae for $a_{E_j}(p)$ for $p$ prime in order to understand $a_{E_j}(n)$ for all $n\geq 1$.
\begin{theorem}
We have the following formulae for primes $p \nmid N$, where $N$ is the conductor.
\begin{align*}

    a_{E_1}(p) &= \begin{cases} 0 & \text{ if } p \equiv 3 \pmod4 \\ (-1)^{n + m}(4n + 2) & \text{ if } p \equiv 1 \pmod4, p = (2n + 1)^2 + 4m^2, n, m \ge 0 \end{cases} \\
    a_{E_2}(p) &= \begin{cases} 0 & \text{ if } p \equiv 3 \pmod4 \\ 2p\Big(\frac{p}{3}\Big) & \text{ if } p \equiv 1 \pmod{3}, p = n^2 + 3m^2, \end{cases} \\
    a_{E_3}(p) &= \begin{cases} 0 & \text{ if } p \equiv 3 \pmod4 \\ (-1)^{n}(4n + 2) & \text{ if } p \equiv 1 \pmod4, p = (2n + 1)^2 + 4m^2, n, m \ge 0 \end{cases}
\end{align*}
\end{theorem}
\begin{proof}
Follows from the $q$-series infinite product identities in Proposition \ref{identities}.
\end{proof}
We observe that the Fourier coefficients of these weight 2 newforms represented by eta quotients with complex multiplication give rise to primes represented as binary quadratic forms. Thus, to study these primes, we can instead study the distribution of the Fourier coefficients $\{a_{E_j} (p)\}$.

\section{Preliminary manipulations}
Let
\[
E:y^2 = x^3+ax^2+bx+c
\]
be an elliptic curve defined over ${\mathbb Q}$ having conductor $N$.  Suppose that $E/{\mathbb Q}$ has complex multiplication by an imaginary quadratic field $K$ having ring of integers $\mathcal{O}_K$, discriminant $D$, and absolute norm $\mathrm{N}=\mathrm{N}_{K/\mathbb{Q}}$; concretely, we have $\mathrm{N}\mathfrak{a}=|\mathcal{O}_K/\mathfrak{a}|$ for a nonzero integral ideal $\mathfrak{a}\subseteq\mathcal{O}_K$.  Each Such field $K$ must be of the form ${\mathbb Q}(\sqrt{-d})$ where
\[
d\in\{-1, -2, -3, -7, -11, -19, -43, -67, -163\},
\]
each of which has class number one.  Thus, the integral ideals of $\mathcal{O}_K$ are principally generated.

For a prime $p\nmid N$, we recast the Hasse bound as
\[
p+1-\#E({\mathbb F}_p)=2\sqrt{p}\cos\theta_p.
\]
Given a subinterval $I\subseteq[0,\pi]$ with indicator function $\mathbf{1}_I$ and $x>DN$, we study
\begin{equation}
\label{eqn:sec3sum_1}
\sum_{\substack{x<p\leq x+h \\ \theta_p\in I}}\mathbf{1}_{I}(\theta_p)\log p.
\end{equation}

\subsection{Preliminary Fourier analysis}

Recall that $p+1=\#E({\mathbb F}_p)$ (or, equivalently, $\theta_p=\pi/2$) if and only if $p$ is inert in $K$.  Therefore, we decompose \eqref{eqn:sec3sum_1} as
\begin{equation}
\label{eqn:sec3sum_2}
\sum_{\substack{x<p\leq x+h \\ \theta_p\in I-\{\frac{\pi}{2}\} \\ \textup{$p$ splits in $K$}}}\mathbf{1}_{I}(\theta_p)\log p+\mathbf{1}_{\frac{\pi}{2}\in I}\sum_{\substack{x<p\leq x+h \\ \textup{$p$ is inert in $K$}}}\log p.
\end{equation}
If the interior of $I$ contains $\frac{\pi}{2}$, then there exist intervals $I_1$ and $I_2$ such that we have the disjoint union
\[
I = I_1\cup \{\pi/2\}\cup I_2.
\]
Suppose now that $J\subseteq[0,\pi]$ is an open subinterval that does not contain $\pi/2$ in its interior.

\begin{lemma}
	\label{lem:BS}
	Let $M\geq 1$ be an integer, and let $J\subseteq[0,\pi]$ be a subinterval.  There exist trigonometric polynomials
	\[
	S_{M}^-(\theta) = \sum_{|m|\leq M}b_m^- e^{i m\theta},\qquad S_{M}^+(\theta) = \sum_{|m|\leq M}b_m^+ e^{i m\theta}
	\]
	such that the following properties hold.
	\begin{enumerate}
		\item If $\theta\in[0,\pi]$, then $S_M^-(\theta)\leq\mathbf{1}_J(\theta)\leq S_M^+(\theta)$.
		\item If $0<|m|\leq M$, then $b_m^{\pm}=b_{-m}^{\pm}$.
		\item We have the bounds
		\begin{equation}
		\label{eqn:first_Fourier}
		\Big|b_0^{\pm} - \frac{|J|}{\pi}\Big|\ll\frac{1}{M}.
		\end{equation}
		\item If $0<|m|\leq M$, then we have the bounds
		\[
		|b_m^{\pm}|\ll \frac{1}{M}+\min\Big\{|J|,\frac{1}{|m|}\Big\}.
		\]
	\end{enumerate}
\end{lemma}
\begin{proof}
	See \cite[Lecture 1]{Montgomery}.
\end{proof}

It follows from Lemma \ref{lem:BS} that
\[
\sum_{|m|\leq M}b_m^- \sum_{\substack{x<p\leq x+h \\ \textup{$p$ splits in $K$}}} e^{i m\theta_p}\log p \leq \sum_{\substack{x<p\leq x+h \\ \theta_p\in J \\ \textup{$p$ splits in $K$}}}\mathbf{1}_{J}(\theta_p)\log p\leq \sum_{|m|\leq M}b_m^+ \sum_{\substack{x<p\leq x+h \\ \textup{$p$ splits in $K$}}} e^{i m\theta_p}\log p.
\]
The bounds on $|b_m^{\pm}|$ and the relation between $b_m^{\pm}$ and $b_{-m}^{\pm}$ imply that
\begin{multline*}
\Big|\sum_{\substack{x<p\leq x+h \\ \theta_p\in J \\ \textup{$p$ splits in $K$}}}\mathbf{1}_{J}(\theta_p)\log p - \frac{|J|}{\pi}\sum_{\substack{x<p\leq x+h \\ \textup{$p$ splits in $K$}}}\log p\Big|\\
\ll \frac{1}{M}\sum_{\substack{x<p\leq x+h \\ \textup{$p$ splits in $K$}}}\log p+\sum_{1\leq m\leq M}\Big(\frac{1}{M}+\min\Big\{|J|,\frac{1}{|m|}\Big\}\Big)\Big|\sum_{\substack{x<p\leq x+h \\ \textup{$p$ splits in $K$}}}e^{im\theta_p}\log p\Big|.
\end{multline*}
If $\chi_D$ denotes the primitive quadratic Dirichlet character associated to $K$ and $p>DN$, it follows that
\[
\frac{1+\chi_D(p)}{2}=\begin{cases}
	1&\mbox{if $p$ splits in $K$,}\\
	0&\mbox{if $p$ is inert in $K$}
\end{cases},\qquad \frac{1-\chi_D(p)}{2}=\begin{cases}
	0&\mbox{if $p$ splits in $K$,}\\
	1&\mbox{if $p$ is inert in $K$.}
\end{cases}
\]
Defining $\chi_0$ to be the trivial Dirichlet character modulo 1, we it follows from the discussion above that
\begin{multline}
\label{eqn:sec3sum_3}
\Big|\sum_{\substack{x<p\leq x+h \\ \theta_p\in I}}\log p - \Big(\frac{1}{2}\mathbf{1}_{\frac{\pi}{2}\in I}+\frac{|I|}{2\pi}\Big)h\Big|\\
\ll\frac{1}{M}\sum_{\substack{x<p\leq x+h \\ \textup{$p$ splits in $K$}}}\log p+ \sum_{1\leq m\leq M}\Big(\frac{1}{M}+\min\Big\{|I|,\frac{1}{|m|}\Big\}\Big)\Big|\sum_{\substack{x<p\leq x+h \\ \textup{$p$ splits in $K$}}}e^{im\theta_p}\log p\Big|\\
+(\mathbf{1}_{\frac{\pi}{2}\in I}+|I|)\sum_{\chi\in\{ \chi_D,\chi_0\}}\Big|\sum_{x<p\leq x+h}\chi(p)\log p-\delta_{\chi}h\Big|,
\end{multline}
where $\delta_{\chi}=1$ if $\chi=\chi_0$ and $\delta_{\chi}=0$ if $\chi=\chi_D$.

\subsection{Hecke Gr{\"o}ssencharacters}

We introduce a crucial connection between the angles $\theta_p$ at primes $p$ that split completely in $K$ and certain infinite-order characters defined on integral ideals of $K$.

\begin{lemma}
\label{lem:Grossencharacter}
	Let $w$ be the number of roots of unity in $K$.  For each integer $m\neq 0$, there exists an integral ideal $\mathfrak{m}_m$ (depending only on $K$ and the residue class of $m$ modulo $w$) and a Hecke Gr{\"o}ssencharacter modulo $\mathfrak{m}_m$ with frequency $m$ such that if $p$ splits completely in $K$, so that there exists a prime ideal $\mathfrak{p}$ of $\mathcal{O}_K$ such that $(p)=\mathfrak{p}\overline{\mathfrak{p}}$, then
\[
\xi_{m}(\mathfrak{p}) = e^{im\theta_p}.
\]
\end{lemma}
\begin{proof}
See \cite[Section 2]{Sutherland}.  The discussion therein relies crucially on \cite[Theorem II.10.5]{Silverman}, which was originally proved by Deuring.  To provide an explicit example, when $E$ is the elliptic curve $y^2=x^3-x$ from the introduction, then $K={\mathbb Q}(i)$, and for each $m\geq 1$, we define
\[
\mathfrak{m}_m=\begin{cases}
	\mathcal{O}_K &\mbox{if $m\equiv 1\pmod{4}$,}\\
	(1+i)^2&\mbox{if $m\equiv 3\pmod{4}$,}\\
	(1+i)^3&\mbox{if $m$ is even.}
\end{cases}
\]
If $\mathfrak{a}$ is a nonzero integral ideal of $\mathcal{O}_K$ generated by $\alpha\in\mathcal{O}_K$ with $\alpha\equiv  1\pmod{\mathfrak{m}_m}$, then we let
\[
\xi_{m}(\mathfrak{a}) = \begin{cases}
	(\alpha/|\alpha|)^{m-1}&\mbox{if $\mathfrak{a}$ and $\mathfrak{m}_m$ are coprime,}\\
	0&\mbox{otherwise.}
\end{cases}
\]
We multiplicatively extend $\xi_{m}$ to other nonzero fractional ideals $\mathfrak{a}$ that are coprime to $\mathfrak{m}_m$, and we extend $\xi_{m}$ to all other nonzero fractional ideals by sending them to zero.  This defines a primitive Hecke Grossencharacter modulo $\mathfrak{m}_m$ for all $m\geq 1$.  For $m\geq 1$, we have $\xi_{-m}=\overline{\xi_{m}}$.
\end{proof}

Note that if $\mathfrak{p}$ is a prime ideal of $\mathcal{O}_K$ such that there exists a prime $p$ satisfying $(p)=\mathfrak{p}\overline{\mathfrak{p}}$, then $\mathrm{N}\mathfrak{p}=p$.  For all other prime ideals of $K$, there exists a prime $q$ such that $\mathrm{N}\mathfrak{p}=q^2$.  The contribution from such primes is trivially bounded by $O(\sqrt{x}\log x)$ by the prime number theorem.  It follows that the right hand side of \eqref{eqn:sec3sum_3} is
\begin{multline}
\label{eqn:sec3sum_4}
\ll\frac{1}{M}\sum_{x<p\leq x+h }\log p+ \sum_{1\leq m\leq M}\Big(\frac{1}{M}+\min\Big\{|I|,\frac{1}{|m|}\Big\}\Big)\Big|\sum_{x<\mathrm{N}\mathfrak{p}\leq x+h}\xi_{m}(\mathfrak{p})\log \mathrm{N}\mathfrak{p}\Big|\\
+|I|\cdot\Big|\sum_{x<p\leq x+h}\chi_D(p)\log p\Big|+\sqrt{x}\log x.
\end{multline}

For an integral ideal $\mathfrak{a}$ of $\mathcal{O}_K$, we define
\[
\Lambda_K(\mathfrak{a}) = \begin{cases}
	\log{\mathrm{N}}\mathfrak{p}&\mbox{if there exists a prime ideal $\mathfrak{p}$ and an integer $j\geq 1$ such that ${\mathfrak a}=\mathfrak{p}^j$,}\\
	0&\mbox{otherwise.}
\end{cases}
\]
It will be convenient for us to bound the error in approximating a sum over $\xi_{m}(\mathfrak{p})\log{\mathrm{N}}\mathfrak{p}$ with a sum over $\xi_{m}({\mathfrak a})\Lambda_K({\mathfrak a})$. In particular, we want to bound
\[
\Big|\sum_{x < {\mathrm{N}}{\mathfrak a} \le x+h}\xi_{m}({\mathfrak a})\Lambda({\mathfrak a}) - \sum_{x < {\mathrm{N}}\mathfrak{p} \le x+h}\xi_{m}({\mathfrak p})\log{{\mathrm{N}}\mathfrak{p} }\Big|
\]
First, note that $|\xi_m({\mathfrak a})|\leq1$, so $|\xi_{m}({\mathfrak a})\Lambda({\mathfrak a})| \le \log{{\mathrm{N}}\mathfrak{p} }$ if ${\mathfrak a}$ is a power of a prime ideal ${\mathfrak p},$ and is 0 otherwise. We rewrite the above as
\begin{align*}
\Big|\sum_{j=1}^{\infty}\sum_{x < {\mathrm{N}}\mathfrak{p} ^j \le x+h}\xi_{m}({\mathfrak p}^j)\log{{\mathrm{N}}\mathfrak{p} } - \sum_{x < {\mathrm{N}}\mathfrak{p} \le x+h}\xi_{m}({\mathfrak p})\log{{\mathrm{N}}\mathfrak{p} }\Big| &= \Big| \sum_{j=2}^{\infty}\sum_{x < {\mathrm{N}}\mathfrak{p} ^j \le x+h}\xi_{m}({\mathfrak p}^j)\log{{\mathrm{N}}\mathfrak{p} } \Big| \\
&\le \sum_{j=2}^{\infty}\sum_{x < {\mathrm{N}}\mathfrak{p} ^j \le x+h}\xi_{m}({\mathfrak p}^j)\log{{\mathrm{N}}\mathfrak{p} } \\
&\ll (\log{x})^2 \sum_{x < {\mathrm{N}}\mathfrak{p} ^2 \le x+h}\log{{\mathrm{N}}\mathfrak{p} } \\
&\ll (\log{x})^2\sum_{\sqrt{x} < {\mathrm{N}}\mathfrak{p} \le \sqrt{x}+\frac{2h}{\sqrt{x}}}1
\end{align*}
By \cite[Proposition 2]{Grenie-Molteni-Perelli},
this is bounded by
\begin{equation*}
    \ll (\log x)^2 \frac{h}{\sqrt{x}\log x} =  \frac{h}{\sqrt{x}}\log x
\end{equation*}
Then,
\begin{multline}
\label{eqn:fourier_coeffs_accumulate}
\sum_{\substack{m \in {\mathbb Z} \\ |m| \le M}}|b_m^{\pm}|\Big|\sum_{x < {\mathrm{N}}{\mathfrak a} \le x+h}\xi_{m}({\mathfrak a})\Lambda({\mathfrak a}) - \sum_{x < {\mathrm{N}}\mathfrak{p} \le x+h}\xi_{m}({\mathfrak p})\Lambda({\mathfrak p})\Big| \\
\ll \frac{h\log{x}}{\sqrt{x}} \sum_{\substack{m \in {\mathbb Z} \\ 0<|m| \le M}}\Big(\frac{1}{M} + \min\Big(\frac{1}{|m|}, |I| \Big) \Big) \\
\ll \frac{h\log{x}}{\sqrt{x}}\log M = x^{1/2 - \delta'}(\log x)^2.
\end{multline}
It follows that \eqref{eqn:sec3sum_4} is
\begin{multline}
\label{eqn:sec3sum_5.1}
\ll\frac{1}{M}\sum_{x<p\leq x+h }\log p+ \sum_{1\leq m\leq M}\Big(\frac{1}{M}+\min\Big\{|I|,\frac{1}{|m|}\Big\}\Big)\Big|\sum_{x<\mathrm{N}\mathfrak{a}\leq x+h}\xi_{m}(\mathfrak{a})\Lambda_K({\mathfrak a})\Big|\\
+|I|\cdot\Big|\sum_{x<p\leq x+h}\chi_D(p)\log p\Big|+\sqrt{x}\log x.
\end{multline}
Recalling the classical von Mangoldt function
\[
\Lambda(n)=\begin{cases}
	\log p&\mbox{if $n=p^k$ for some prime $p$ and some integer $k\geq 1$,}\\
	0&\mbox{otherwise}
\end{cases}
\]
along with the Chebyshev bounds for the prime counting function, we  find that \eqref{eqn:sec3sum_5.1} is
\begin{multline}
\label{eqn:sec3sum_5}
\ll\frac{1}{M}\sum_{x<p\leq x+h }\log p+ \sum_{1\leq m\leq M}\Big(\frac{1}{M}+\min\Big\{|I|,\frac{1}{|m|}\Big\}\Big)\Big|\sum_{x<\mathrm{N}\mathfrak{a}\leq x+h}\xi_{m}(\mathfrak{a})\Lambda_K({\mathfrak a})\Big|\\
+|I|\cdot\Big|\sum_{x<p\leq x+h}\chi_D(n)\Lambda(n)\Big|+\sqrt{x}\log x.
\end{multline}
For expositional clarity, we defer our handling of the sum over $\chi_D(n)\Lambda(n)$ to the end of our proofs, and we will only address it briefly.\footnote{The extra contribution from the sum over $\chi_D(n)\Lambda(n)$ is much simpler to handle than the sum over Hecke Gr{\"o}ssencharacters, but it is handled independently from the Hecke Gr{\"o}ssencharacter contribution.}

\section{$L$-functions of Hecke Gr{\"o}ssencharacters}

In order to bound \eqref{eqn:sec3sum_5} efficiently, we introduce the theory of $L$-functions, starting with a classical result of Hecke \cite{hecke}.

\begin{lemma}
\label{lem:Hecke_L-function}
	Let $m$ be a nonzero integer, and let $\xi_m\pmod{\mathfrak{m}_m}$ be as in Lemma \ref{lem:Grossencharacter}.  Define
	\[
	L(s,\xi_m) = \prod_{\mathfrak{p}}(1-\xi_m(\mathfrak{p}){\mathrm{N}}\mathfrak{p}^{-s})^{-1}.
	\]
	The above Euler product converges absolutely for $\mathrm{Re}(s)>1$.  Moreover, if we define
	\[
	\Lambda(s,\xi)=((2\pi)^{-2}D{\mathrm{N}}\mathfrak{m}_m)^{\frac{s}{2}}\Gamma\Big(s+\frac{m}{2}\Big)L(s,\xi),
	\]
	where $\Gamma(s)$ is the complex-analytic extension of the factorial, then $\Lambda(s,\xi)$ is an entire function of order one, and there exists a complex number $W(\xi_m)$ of modulus one such that
	\[
	\Lambda(s,\xi)=W(\xi)\Lambda(1-s,\overline{\xi}).
	\]
\end{lemma}
\begin{remark}
The integer $D{\mathrm{N}}\mathfrak{m}_m$ is not pertinent in our proofs because $D$ is fixed (since $E/{\mathbb Q}$ is fixed) and $\mathfrak{m}_m$ depends only on $K$ (which is fixed) and the residue class of $m$ modulo the number of roots of unity in $K$, and the number of such residue classes is fixed.
\end{remark}

The Euler product that defines $L(s,\xi)$ converges absolutely for $\mathrm{Re}(s)>1$, so it follows that $L(s,\xi)\neq 0$ in that region.  By the functional equation of $\Lambda(s,\xi)$, it follows that $L(s,\xi)\neq 0$ for $\mathrm{Re}(s)<0$ except at $-j-\frac{m}{2}$, where $j\geq 0$ is an integer.  These trivial zeros arise as poles of the gamma function.  Because $\Lambda(s,\xi)$ is entire of order one, it exhibits a Hadamard factorization
\[
\Lambda(s,\xi)=\prod_{\rho}\Big(1-\frac{s}{\rho}\Big)e^{\frac{s}{\rho}},
\]
where $\rho=\beta+i\gamma$ denotes a nontrivial zero of $L(s,\xi)$.  These zeros all satisfy $0\leq\beta\leq 1$ and $\gamma\in{\mathbb R}$.  The nontrivial zeros are directly related to the partial sums of $\xi_m({\mathfrak a})\Lambda_K({\mathfrak a})$ by means of the so-called ``explicit formula".

\begin{lemma}
	\label{lem:explicit_formula}
	If $1\leq m\leq M\leq x$ and $x^{1-\delta}\leq h\leq x$, then
	\[
	\sum_{x<{\mathrm{N}}{\mathfrak a}\leq x+h}\xi_m({\mathfrak a})\Lambda_K({\mathfrak a}) = -\sum_{\substack{\rho=\beta+i\gamma \\ |\gamma|\leq Mx/h \\ 0\leq\beta\leq 1}}\frac{(x+h)^{\rho}-x^{\rho}}{\rho}+O\Big(\frac{h(\log x)^2}{M}\Big).
	\]
\end{lemma}
\begin{proof}
	It follows from \cite[Theorem 12.5]{Iwaniec} that $L(s,\xi_m)$ is in fact the $L$-function associated to a holomorphic cuspidal Hecke eigenform of weight $m+1$ and level $D{\mathrm{N}}\mathfrak{m}$ (which, as we already observed, is uniformly bounded).  This is a degree 2 $L$-function defined over ${\mathbb Q}$ whose analytic conductor $\mathfrak{q}_m$ (per \cite[Equation 5.7]{Iwaniec-Kowalski}) satisfies $\log \mathfrak{q}_m\asymp \log m\ll \log M\ll \log x$.  By \cite[Equation 5.53]{Iwaniec-Kowalski}, it follows that
	\[
	\sum_{{\mathrm{N}}{\mathfrak a}\leq x}\xi_m({\mathfrak a})\Lambda_K({\mathfrak a}) = -\sum_{\substack{\rho=\beta+i\gamma \\ |\gamma|\leq Mx/h \\ 0\leq\beta\leq 1}}\frac{x^{\rho}-1}{\rho}+O\Big(\frac{h(\log x)^2}{M}\Big).
	\]
	The desired result follows from taking the difference between the above expression at $x$ and at $x+h$.
\end{proof}

While our focus here is on Hecke Gr{\"o}ssencharacters, there is a corresponding theory for Dirichlet characters which was established long before the work of Hecke.  We summarize the key results, all of which are proved in \cite{davenport}.

\begin{theorem}
Let $\chi\in \{\chi_0,\chi_D\}$ be as above.  Let $q=D$ if $\chi=\chi_D$ and $q=1$ if $\chi=\chi_0$  Define
\[
L(s,\chi) = \prod_p (1-\chi(p)p^{-s})^{-1}.
\]
The above Euler product converges absolutely for $\mathrm{Re}(s)>1$.  Moreover, if we define
\[
\Lambda(s,\chi) = \pi^{-s/2} q^{s/2}\Gamma\Big(\frac{s+\frac{1-\chi(-1)}{2}}{2}\Big)L(s,\chi)m
\]
then $\Lambda(s,\chi)$ is an entire function of order one, and there exists a complex number $W(\chi)$ of modulus one such that
\[
\Lambda(s,\chi)=W(\chi)\Lambda(1-s,\chi).
\]
If $\rho=\beta+i\gamma$ denotes a nontrivial zero of $L(s,\chi)$ with $0\leq\beta\leq 1$, and if $x^{1-\delta}\leq h\leq x$, then
\[
\sum_{x<n\leq x+h} \chi(n)\Lambda(n) = -\sum_{\substack{\rho=\beta+i\gamma \\ |\gamma|\leq Mx/h \\ 0\leq\beta\leq 1}}\frac{(x+h)^{\rho}-x^{\rho}}{\rho}+O\Big(\frac{h(\log x)^2}{M}\Big).
\]
\end{theorem}

\subsection{Preliminary reductions}

By a calculation nearly the same as \eqref{eqn:fourier_coeffs_accumulate}, we deduce that \eqref{eqn:sec3sum_5} is
\begin{multline}
	\label{eqn:sec4sum_1}
	\ll\frac{1}{M}\sum_{x<p\leq x+h }\log p+ \sum_{1\leq m\leq M}\Big(\frac{1}{M}+\min\Big\{|I|,\frac{1}{|m|}\Big\}\Big)\sum_{\substack{\rho=\beta+i\gamma \\ L(\rho,\xi_m)=0 \\ |\gamma|\leq Mx/h \\ 0\leq\beta\leq 1}}\Big|\frac{(x+h)^{\rho}-x^{\rho}}{\rho}\Big|\\
+(\mathbf{1}_{\frac{\pi}{2}\in I}+|I|)\sum_{\chi\in\{\chi_0,\chi_D\}}\sum_{\substack{\rho=\beta+i\gamma \\ L(s,\chi)=0 \\ |\gamma|\leq Mx/h \\ 0\leq\beta\leq 1}}\Big|\frac{(x+h)^{\rho}-x^{\rho}}{\rho}\Big|+\sqrt{x}\log x+\frac{h(\log x)^3}{M}.
\end{multline}
In light of the bound
\[
\Big|\frac{(x+h)^{\rho}-x^{\rho}}{\rho}\Big|=\Big|\int_{x}^{x+h}t^{\rho-1}dt\Big|\leq \int_x^{x+h}t^{\beta-1}dt\ll hx^{\beta-1},
\]
we find that \eqref{eqn:sec4sum_1} is
\begin{multline}
	\label{eqn:sec4sum_2}
	\ll\frac{1}{M}\sum_{x<p\leq x+h }\log p+ h\sum_{1\leq m\leq M}\Big(\frac{1}{M}+\min\Big\{|I|,\frac{1}{|m|}\Big\}\Big)\sum_{\substack{\rho=\beta+i\gamma \\ L(\rho,\xi_m)=0 \\ |\gamma|\leq Mx/h \\ 0\leq\beta\leq 1}}x^{\beta-1}\\
+(\mathbf{1}_{\frac{\pi}{2}\in I}+|I|)h\sum_{\chi\in\{\chi_0,\chi_D\}}\sum_{\substack{\rho=\beta+i\gamma \\ L(s,\chi)=0 \\ |\gamma|\leq Mx/h \\ 0\leq\beta\leq 1}}x^{\beta-1}+\sqrt{x}\log x+\frac{h(\log x)^3}{M}.
\end{multline}
In order to ensure that our Fourier coefficient bounds from Lemma \ref{lem:BS} are nontrivial, we make the assumption
\[
|I|\gg M^{-1}
\]
so that \eqref{eqn:sec4sum_2} is
\begin{equation}
	\label{eqn:sec4sum_3}
	\ll\frac{1}{M}\sum_{x<p\leq x+h }\log p+ (\mathbf{1}_{\frac{\pi}{2}\in I}+|I|)h\sum_{\substack{\rho=\beta+i\gamma \\ |\gamma|\leq Mx/h \\ 0\leq\beta\leq 1}}x^{\beta-1}+\frac{h(\log x)^3}{M}+\sqrt{x}\log x,
\end{equation}
where $\rho=\beta+i\gamma$ ranges over all zeros of $L(s,\chi_0)$, $L(s,\chi_D)$, and the $L$-functions $L(s,\xi_m)$ with $1\leq m\leq M$.  It follows from the work of Montgomery and Vaughan \cite[Equation 1.12]{M-V} that if $h\geq x^{1-\delta}$, then
\[
\sum_{x<p\leq x+h}\log p\ll h.
\]
Consequently, if $h\geq M\sqrt{x}$, then \eqref{eqn:sec4sum_3} is
\begin{equation}
	\label{eqn:sec4sum_4}
	\ll\frac{h(\log x)^3}{M}+ (\mathbf{1}_{\frac{\pi}{2}\in I}+|I|)h\sum_{\substack{\rho=\beta+i\gamma \\ |\gamma|\leq Mx/h \\ 0\leq\beta\leq 1}}x^{\beta-1} \ll\frac{h(\log x)^3}{M}+ (\mathbf{1}_{\frac{\pi}{2}\in I}+|I|)h\sum_{\substack{\rho=\beta+i\gamma \\ |\gamma|\leq Mx/h \\ \frac{1}{2}\leq\beta\leq 1}}x^{\beta-1},
\end{equation}
The last step uses the consequence of the functional equations for $L(s,\xi_m)$ and $L(s,\chi)$ that if $\beta+i\gamma$ is a zero, then so is $1-\beta+i\gamma$.

\subsection{Zeros of Hecke Gr{\"o}ssencharacter $L$-functions}

We now proceed as in the work of Hoheisel.  Define
\begin{multline*}
N(\sigma,M,T):=\sum_{1\leq m\leq M}\#\{\rho=\beta+i\gamma\colon L(\rho,\xi_m)=0,~|\gamma|\leq T,~\beta\geq\sigma\}\\
+\sum_{\chi\in\{\chi_0,\chi_D\}}\#\{\rho=\beta+i\gamma\colon L(\rho,\chi)=0,~|\gamma|\leq T,~\beta\geq\sigma\}.
\end{multline*}
Then \eqref{eqn:sec4sum_4} is
\begin{equation}
\label{eqn:sec4sum_5}
\ll\frac{h(\log x)^3}{M}+ (\mathbf{1}_{\frac{\pi}{2}\in I}+|I|)h (\log x)\max_{\frac{1}{2}\leq \sigma\leq 1}x^{\sigma-1}N(\sigma,M,Mx/h).
\end{equation}
In order to show that \eqref{eqn:sec4sum_5} is small, we will make use of a zero-free region and zero density estimate.  The zero-free region is a result of Coleman in \cite{colemanZFR}.
\begin{lemma}
\label{ZFR}
Let $m\geq 1$.  There exists a constant $c > 0$ depending only on $E$ such that $L(s,\xi_m)\neq 0$ in the region
\[
\mathrm{Re}(s) \ge 1 - \frac{c}{(\log (|\mathrm{im}(s)|+3)|m|)^{2/3}  (\log \log (|\mathrm{im}(s)|+3)|m|)^{1/3}}.
\]
\end{lemma}

We apply Lemma \ref{ZDE} to \eqref{eqn:sec4sum_5} and conclude that it is
\begin{equation}
	\label{eqn:sec4sum_6}
\ll\frac{h(\log x)^3}{M}+ (\mathbf{1}_{\frac{\pi}{2}\in I}+|I|)h (\log x)\max_{\frac{1}{2}\leq \sigma\leq 1-\frac{c}{(\log M^2 x/h)^{2/3}(\log\log M^2 x/h)^{1/3}}}x^{\sigma-1}N(\sigma,M,Mx/h).
\end{equation}

We use a deep {\it zero density estimate}  for Hecke Gr{\"o}ssencharacter $L$-functions due to Coleman \cite[Corollary 8.2]{coleman1990} verifying that $N(\sigma,M,T)$ becomes very small as $\sigma\to 1^-$.  We use this as a strong substitute for the yet-unproven generalized Riemann hypothesis for the family of Hecke Gr{\"o}ssencharacter $L$-functions.
\begin{lemma}
\label{ZDE}
For all $\epsilon>0$, there exists a constant $B>0$ such that
\[
N(\sigma,M,T) \ll_{\epsilon} \max\{M,T\}^{(\frac{24+\epsilon}{5})(1 - \sigma)}(\log{T})^B
\]
for $\frac{1}{2}\le \sigma \le 1$.
\end{lemma}

\section{Proof of Theorem \ref{thm:main_theorem}}

Let $\epsilon>0$ be small.  We apply Lemma \ref{ZDE} to \eqref{eqn:sec4sum_6} to achieve the bound
\begin{multline*}
	(\log x)\max_{\frac{1}{2}\leq \sigma\leq 1-\frac{c}{(\log M^2 x/h)^{2/3}(\log\log M^2 x/h)^{1/3}}}x^{\sigma-1}N(\sigma,M,Mx/h)\\
	\ll_{\epsilon} (\log x)^{B+1}\max_{\frac{1}{2}\leq \sigma\leq 1-\frac{c}{(\log M^2 x/h)^{2/3}(\log\log M^2 x/h)^{1/3}}}\Big(\frac{(Mx/h)^{(24+\epsilon)/5}}{x}\Big)^{1-\sigma}.
\end{multline*}
If $h\geq x^{1-\delta}$ and $M\leq x^{\theta}$, then we assume that
\[
\theta+\delta\leq \frac{5}{24}-\epsilon,\qquad \log(M^2 x/h)\asymp\log x
\]
so that the above maximum is achieved when $\sigma$ is largest.  We find that there exists an absolute constant $c'>0$, depending on $E$, such that
\begin{align*}
&(\log x)^{B+1}\max_{\frac{1}{2}\leq \sigma\leq 1-\frac{c}{(\log M^2 x/h)^{2/3}(\log\log M^2 x/h)^{1/3}}}\Big(\frac{(Mx/h)^{(24+\epsilon)/5}}{x}\Big)^{1-\sigma}\\
&\ll (\log x)^{B+1}\max_{\frac{1}{2}\leq \sigma\leq 1-\frac{c'}{(\log x)^{2/3}(\log\log x)^{1/3}}} x^{-\frac{\epsilon}{120}(1-\sigma)}\\
&\ll (\log x)^{B+1} x^{-\frac{c'\epsilon}{120(\log x)^{2/3}(\log\log x)^{1/3}}}\\
&\ll \exp\Big(-\frac{c'\epsilon (\log x)^{1/3}}{240(\log\log x)^{1/3}}\Big).
\end{align*}
Therefore, \eqref{eqn:sec4sum_6} is
\[
\ll\frac{h(\log x)^3}{M}+ (\mathbf{1}_{\frac{\pi}{2}\in I}+|I|)h \exp\Big(-\frac{c'\epsilon (\log x)^{1/3}}{240(\log\log x)^{1/3}}\Big).
\]
If $\epsilon_1>0$ and $\epsilon_2>0$ are small and we choose $|I|\geq x^{\epsilon_1}/M$, $M\leq x^{\theta}$, $h\geq x^{1-\delta+\epsilon_2}$, and $\theta+\delta\leq \frac{5}{24}-\epsilon$, then we conclude that the above display is
\[
\ll (\mathbf{1}_{\frac{\pi}{2}\in I}+|I|)h \exp\Big(-\frac{c'\epsilon (\log x)^{1/3}}{240(\log\log x)^{1/3}}\Big).
\]
Upon rescaling $\epsilon$, $\epsilon_1$, and $\epsilon_2$, we find that if $\delta>0$ and $\delta'>0$ are fixed numbers such that
\[
h\geq x^{1-\delta},\qquad |I|\geq x^{-\delta'},\qquad \delta+\delta'<\frac{5}{24},
\]
then there exists a constant $c''>0$ (depending on $\delta$, $\delta'$, and $E$) such that
\[
\sum_{\substack{\theta_p\in I \\ x<p\leq x+h}}\log p = \Big(\frac{\mathbf{1}_{\frac{\pi}{2}\in I}}{2}+\frac{|I|}{2\pi}h\Big)\Big(1+O\Big(\exp\Big(-\frac{c''(\log x)^{1/3}}{(\log\log x)^{1/3}}\Big)\Big)\Big),
\]
as desired.

\section{Further extensions}

We now describe a natural extension of our work to the study of Fourier coefficients of holomorphic cuspidal newforms.  Let
\[
f(z) = \sum_{n=1}^{\infty}a_f(n) e^{2\pi inz}
\]
be the Fourier series of a holomorphic cusp form of even integral weight $k\geq 2$ that transforms under the a congruence subgroup $\Gamma_0(N)\subseteq \mathrm{SL}_2(\mathbb{Z})$.  Suppose that $f$ is an eigenform of all of the Hecke operators, and that it is in fact a newform. Each of the $\eta$-quotients in \eqref{eqn:newform_examples} are examples of weight 2 newforms with complex multiplication (i.e., newforms with the property that there exists an imaginary quadratic field $K$ such that for a prime $p$, $a_f(p)=0$ if and only if $p$ is inert in $K$).   Unlike the case for newforms associated to elliptic curves, it could be the case that $K$ has a class number larger than 1, in which case the prime ideals of $K$ are no longer principally generated.

Generalizing what we did for elliptic curves, one could use the Deligne bound
\[
|a_f(p)|\leq 2p^{\frac{k-1}{2}}
\]
(which generalizes the Hasse bound that we used before) and thus define $\theta_p\in[0,\pi]$ by
\[
a_f(p) = 2p^{\frac{k-1}{2}}\cos\theta_p.
\]
We can now ask how the angles $\theta_p$ are distributed in the interval $[0,\pi]$.  In order to relate the angles $\theta_p$ to Hecke Gr{\"o}ssencharacters like we did for elliptic curves, we restrict our consideration to the primes $p$ such that $(p)$ is principally generated.  In order to isolate such primes, we use the orthogonality of the characters of the ideal class group of $K$, a finite abelian group with the property that it is trivial if and only if the ring of integers of $K$ has unique factorization.  One can then use relate the prime counting function
\[
\sum_{\substack{x<p\leq x+h \\ \theta_p\in I \\ \textup{$(p)$ principally generated}}}\log p
\]
to the analytic properties of the $L$-functions $L(s,\xi_m)$ twisted by class group characters.  (The class group characters behave in many ways like Dirichlet characters, but they are defined on integral ideals of $K$ instead of integers in $\mathbb{Z}$.)  Ultimately, the distribution of primes we are interested in boils down to an understanding of the distribution of zeros of the aforementioned $L$-functions.  The zero-free region and zero density estimate of Coleman were proved in this level of generality, so our proofs will carry through with the aforementioned adjustments so that we can conclude
\[
\sum_{\substack{x<p\leq x+h \\ \theta_p\in I \\ \textup{$(p)$ principally generated}}}\log p = \frac{1}{h_K}\Big(\frac{\delta_{\frac{\pi}{2}\in I}}{2}+\frac{|I|}{2\pi}\Big)h\Big(1+O\Big(\exp\Big(-c'''\frac{(\log x)^{1/3}}{(\log\log x)^{1/3}}\Big)\Big)\Big),
\]
where $h\geq x^{1-\delta}$; $|I|\geq x^{-\delta'}$; $\delta+\theta<5/24$; $c'''$ is a certain constant depending on $\delta$, $\delta'$, and $f$; and $h_K$ is the class number of $K$ (i.e., the order of the ideal class group of $K$).

\nocite{cochrane}
\bibliographystyle{acm}

redpajama_set_name: RedPajamaArXiv


A four part beneficial series on How to Develop Khushoo`. Prayer is one of the greatest pillars of Islam, and Khushoo` in prayer is required by sharee`ah.
Iblees, the enemy of Allaah, has vowed to mislead and tempt the sons of Adam, by saying: `Then I will come to them from before them and behind them, from their right and from their left` [7:17] And one of the ways he (the accursed) will come to us, is to mislead us in our prayer.


In accord with the attention-for a watch concept, a perpetrator of such a hearth was usually punished by being burned to loss of life. In the early 20th century, Louis Brandeis , later appointed to the United States Supreme Court, became noted for his use of policy-driving information and economics in his briefs , and extensive appendices presenting information that lead a judge to the advocate's conclusion. Most of the Central and Eastern European and East Asian nations also comply with a civil law construction. Although the English authorized system is founded on frequent legislation, that is not to say that statutes are any much less binding.
While there's a normal respect for the regulation, the sense of generosity and compassion that most Haitians possess lends creed to Haiti's cultural values and the way its civil laws have been written and adopted. This Commons Library briefing paper supplies general information about the variety of cohabiting couples, how the regulation applies to cohabitants, and in regards to the Law Commission's proposals for reform. However, if the marriage breaks down, any property owned by you or your associate will probably be taken into account when arriving at a monetary settlement on divorce. In protection of the American criminal justice system, it has roots in English frequent regulation.
If one is really in opposition to being part of an open marriage or open relationship, then one needs to realize that people they may date or develop into involved with may not share that opinion and should expect to be in an open relationship. The human intuition of love, the idea of marriage and a individuals's cultural id is predicated on a Voodoo ideology that values the rules of human decency and acknowledges the necessity for law and order.
Although an armed pupil might doubtlessly stop an lively shooter who enters their classroom, the Campus Carry legislation was not handed as a plan to cease a college capturing in a Texas school, ought to one ever happen sooner or later. By the late Middle Ages, these two legal guidelines, civil and canon, have been taught at most universities and formed the idea of a shared physique of legal thought common to most of Europe. The authorities of the UNITED STATES OF AMERICA as it stands right now, will not be unbiased.


Allergy and Immunology is a medical specialty that treats allergic diseases and issues affecting your immune system.
In addition to treating occasional stings and adverse reactions, our specialists are able to offer a more systematic approach to allergy management for those that suffer from chronic allergies. After examination and testing, our providers can provide treatments that may include preventative medications or immunotherapy. These treatments can help patients overcome or prevent future allergy problems.


Dr. Chethan Sathish has a keen interest in cosmetic surgery which includes hair transplantation, blepharoplasty, facelift, rhinoplasty (nose job), dimple creation, breast augmentation, breast lift, breast reduction, gynecomastia( male breast), liposuction, tummy tuck and abdominoplasty, body contouring surgeries after massive weight loss, chin augmentation, fat grafting, hymenoplasty, vaginoplasty, lip reduction, botox and fillers, tattoo removal and scar revisions.
Dr Chethan and His team was superb which made me to feel as much easier about my paper work as well as treatment at hospital.
Dr Chethan was avaialable all the time before my surgery and even after my surgery till the results outcome.
I was very afraid abou my nose shape and after the surgery iwas very happy to see myself.
Now absolutely my clothes fit to me and i am very much happy to see myself in Mirror. I gain my confidence to built all the way.
Everything and beautiful went well. Finally my poked nose came to shape.
The implant placed in great and i feel complete with good shape and i can wear BRA happily.
Dr Chethan took his time to answer all my questions and made me feel good. The excellent team with care for both Pre op and Post OP.
Very comfort with my decision.
Dr Chethan is awesome and amazing doctor who is very passionate about his work and dedicated tooo so only i got 100% results.


Ever since Microsoft announced its Kinect peripheral for Xbox 360, the world has both loved it and hated it in equal measure. Sure it's great for getting gamers off the couch and it offers something no other console can – controller-free gaming.
The problem is that despite the hardware packing some impressive technology, Kinect has been something of a one trick pony since its release in late 2010. Now though it would appear Kinect could be getting the game that could make all that money worthwhile – and it's not actually a Kinect game.
Forza 4, the fourth (obviously enough) installment in the super popular Forza Motorsport franchise promises to take Kinect to a new level. As eager developers show off in the embedded video, Forza 4 uses Kinect to track players' head movements and then alter the in-game camera accordingly.
What this means in real terms is no more staring at the floor while raving. Players can look left and right to help judge those corners better, or set their car up for an upcoming bend.
The video does a better job of explaining than we do, but it also shows one of the inherent problems. You might be able to move your head, but your eyes will obviously need to stay trained on the screen in front of you – that's if you want to see where you're going.
That one nagging doubt aside and this looks like a great use for our otherwise dust-collecting Kinect.


text:
A Closer Look at Trees
Hero Story - Destinations
Giving a Historic Bird House New Life
Coming in March 2023 to the Smithsonian National Zoo & Conservation Biology Institute in Washington, DC is a new Bird House—an attraction that's sure to impress bird enthusiasts of all kinds. Idea...
Trees are being destroyed worldwide by deforestation, development and the effects of climate change. Botanical gardens are at the forefront of the fight to save them—and a new traveling exhibition at The Huntington invites groups into the conversation.
Out of the Woods: Celebrating Trees in Public Gardens opens at The Huntington Library, Art Collections, and Botanical Gardens on May 19, 2018. Robert Hori, gardens cultural curator and program director, offers an inside look at the exhibition and what it means for The Huntington and its visitors.
Groups Today: Could you tell us a bit about Out of the Woods and its importance?
Robert Hori: Organized by The New York Botanical Garden and the American Society of Botanical Artists, this traveling exhibition of original botanical artworks spotlights one of the planet's most important and beautiful resources—its trees—as cultivated by botanical gardens and arboreta. The exhibition highlights the role public gardens play in engaging visitors with trees and their ecological and utilitarian roles, and also underscores the conservation, research and scholarship being undertaken by these institutions.
From more than 200 submitted entries, 43 artworks were selected for the exhibition, featuring images of trees from small county arboreta alongside those from some of the world's most renowned botanical gardens—including The Huntington.
Working in watercolor, oil, graphite, colored pencil and ink, an international collection of artists has depicted everything from seedpods, branches and bark to an entire forest floor. By bringing these subjects to life through their work, botanical artists create new pathways for communicating the value of plants in contemporary life.
GT: Why was The Huntington Library interested in running this exhibition?
RH: The mission of the Huntington Library, Art Collections, and Botanical Gardens is to promote education and research through its collections. Many visitors to the botanical gardens are so overwhelmed by the natural beauty that surrounds them that they may not realize that we are also an important repository of plants. In the same way that library and art galleries safeguard collections, the botanical gardens collect, study and propagate both common and endangered plants. For example, our Desert Garden features plants that were once commonly found in nature but—due to development—have lost their natural habitat and can only be found in botanical gardens.
GT: What tree species will groups see in the Botanical Gardens that are depicted in Out of the Woods?
RH: Out of the Woods features works by seven artists who are members of the Southern California chapter of the American Society of Botanical Artists. The tree specific to The Huntington is the California Sycamore, depicted by Deborah Friedman.
In the exhibition catalog, Deborah elaborates on her selection:
"This tree filled me with inspiration because of the rich variety of textured material, brilliant magenta female flowers, colorful puzzle shaped bark, and majestic architecture. There was also a sentimental reason for choosing this particular tree. As a child I rode my bike along a ridge while watching red tailed hawks soar through the canyon below where the birds nested in the massive sycamore tree tops. This is a cherished childhood memory."
"I went to the Huntington Library, Art Collections and Botanical Garden for this project because I had attended a fascinating class about trees at the Huntington taught by Jim Folsom, who is the director of Botanical Gardens. The California native sycamores are growing beside an outdoor cafe where Jim presented some of his lecture material, which included information about the sycamores. I have since spent many afternoons at the Huntington wandering the gardens while admiring the tree collections."
GT: What would you like visitors to The Huntington Library to take away from Out of the Woods?
RH: The works in the exhibit feature trees in all of their seasonal beauty and various stages of development. I hope the exhibit will encourage viewers to take a closer look at trees in the gardens and to return to see how they are continuously changing throughout the year.
Photo: Ann S. Hoffenberg, Paperbark Maple (2017), Acer griseum, Rutgers Gardens, New Brunswick, New Jersey. Watercolor on paper, 9 x 13 inches. © Ann S. Hoffenberg. Courtesy of the American Society of Botanical Artists and the New York Botanical Garden.
Edited by Cassie Westrate, staff writer for Groups Today.
Destination Articles
Emerging Destinations: Namibia
Learning at New Heights: Skywalk Observatory


For as long as I can remember, I've wanted to be a mom.
This past November, my doctor suggested going off of birth control for 3 months because of the many adverse effects on my health that I had experienced using the medication. I felt this was the best decision for the time being as well. Jake and I had discussed the possibility of 'just seeing what happened', but quickly decided against it and continued on with the plan that we would try to start a family once I graduated. That plan obviously didn't work out, and honestly, we couldn't be more excited! We know that this was not a mistake and that this is the exact time our son is meant to come to earth. While you know that I am beyond excited for this little boy, here's the part of the story you don't know.
On the morning of January 13th, I went to take my prescriptions as I had done nearly every morning for the past 6 years. However, as I began to lift up the bottles, I felt a force, as if it were a palpable hand, pushing my hand back down. I physically could not pick up my medicine. It was so bizarre to me that I attempted to pick up my medications three more times before realizing that whatever this force was, was very real and that I really was not going to be able to take my medicine that day.
So, I didn't take my medicine and questioned why in the world that would happen or how it could happen at all. It only took about 7 hours from that time for my body to suffer. Intense withdrawals began; my body shook and I was more nauseated than I had been in my whole life. The next day came, same thing. I could not take my medicine. I found it odd and frustrating but continued on with my day. The withdrawals got worse as the days went on, and the next two weeks after I stopped taking my medicine were arguably the hardest of my life. It felt like my body was shutting down. Why was this happening? I didn't want to discuss it with a doctor - I knew it wouldn't make sense why I was doing this (it hardly made sense to me). However, two weeks and one day later, it all became extremely clear.
Throughout those two weeks, I was constantly questioning why I had to go through this. Why in the world could I not take my medication? I would have little thoughts pop in my head that maybe I was pregnant, but I quickly brushed those thoughts away. There was no way I could be pregnant this quick without trying!
But, two weeks and one day after I had stopped taking my medicine, I took a test. I took a pregnancy test that morning because I had a box of them 'just in case'. So, I took the test as more of a "well, it's the last one in the box, might as well get rid of it" sort of notion. Within seconds, the test showed I was pregnant. I was in shock, but at the same time it all made sense. I told Jacob immediately and he was thrilled. We couldn't have been more excited! We were both so surprised, but so overjoyed. We knew immediately that this was the will of God and that this happened for a definite reason. We had both wanted to be parents for so long, and though we had intended on trying to become parents much later on in life, those hesitant thoughts soon melted away.
I'm so beyond thankful for whatever divine intervention caused me to stop taking my medicine. The crazy thing is, after calculating my due date and all parts of the equation, it added up to my conception date being the very day before I stopped taking my medicine. I know without a doubt that the Lord is deeply involved in the very details of our lives. He knew that all three of my prescriptions were deemed unsafe for me to take while pregnant, and intervened so I could have the healthiest possible pregnancy to bring our sweet son to this earth.
My testimony of the healing power of the atonement has grown exponentially since this experience. I always knew that the atonement heals us emotionally, but I always seemed to forget the physical healing powers of the atonement. I still struggle with my depression and anxiety, but so much of it has been lifted. I no longer need any medications to manage my health problems, and I feel that I will never need to take those medications again. My heart feels strong, physically and emotionally. My thoughts of suicide have nearly diminished. My body is healing, because of Him. Because of Him, I can carry this child with confidence.
I never thought I would be free of taking prescriptions - and I definitely don't intend for those that read this to believe that all physical ailments are resolved through the atonement in this life; I do believe that pharmaceuticals can be a necessity and absolute blessing. But for whatever reason, I believe that Heavenly Father saw fit for these ailments to be lifted from me through the atonement, and I am beyond thankful and blessed.
So, there's the part of the story you didn't know - the part that I never thought I'd share. The thing is though, the atonement is so much more than we can possibly comprehend. Miracles surround us daily. The atonement has the power to heal us in all aspects of life: emotional, mental, physical. The healing of bodies is not just found in scripture. It is here, now. I know this more now than ever before. I am continually amazed by the power this gospel truly holds. It is true! It really is.
Congratulations McKell!! I'm so happy for you guys :) I'm glad you shared this event- it's a wonderful example of how tender mercies surround us. And you are brave to share your experience. Thank you for your testimony building post. Best wishes that all continues to go well.


Самое оптимальное сочетание цена - качество. Глупо переплачивать за красивые наклейки и громкие названия.
Lo tomo 3 veces al día, y no siento absolutamente nada. No he notado ningún avance en mis resultados.
ALCAR is a great supplement to include in your routine regardless of your goals. I add three scoops to my protein shake and it doesn't alter the flavor at all. The price is great and I've got quite a bit, even at 3 scoops a day so this represents a great investment. This is now one of my repeat buys.
I take a scoop of this with my morning protein shake and it gives me a great energy and focus boost that lasts the whole day. It's easy to mix and will last you a LONG time! It is unflavoured so it will have a natural sour taste (just like all l-carnitine), and works well to complement a sweet protein shake.
Super product and should be a staple in a fat burning stack! Tastes like sour lemon so adding it to your Pre or Intra would be a good idea( choose a sour tasting flavor like lemon lime or green apple..). Take 1.5g (3 scoops) 2-3 times daily as Dr Jym Stoppani recommends and you will finds amazing results. Consider stacking this with caffeine, green tea, cla, and yohimbine for better results.
Great product for the cost. Amazing difference when i added this to my pre workout shake. The product is unflavored but has a sour taste and smells just like vinegar. Its not all that bad by itself but mix it with something else and you cant tell its there.
I've seen great results with this in combination with a low-carb diet.


Are Full Dentures & Partials the Same?
Everyone vies to have a set of dazzling and perfect teeth and that is what gives you a beautiful smile. Apart from being an eyesore, missing teeth also lead to drifting of the rest of your teeth and they will eventually change position. Subsequently, this can lead to mouth tissue damage and it is also very difficult to brush and floss crooked and misaligned teeth. Tooth decay and periodontal disease are very common in people who have crooked teeth as it is very difficult to maintain high levels of oral hygiene.
Dentures & Partials can be used very effectively to fill all the gaps that are created by any missing teeth. Many people believe that dentures are always an entire set of teeth. The fact is that it is also possible to have dentures & partials that do not cover the entire set. If you have some healthy teeth and only need to fill in the gaps that have been created by missing teeth, partials are the perfect solution for you. We at Brummett and Tallent Cosmetic and Family Dental can provide you with the best set of dentures & partials and we have years of experience in all kinds of dental procedures.
Conventional Partial Dentures- These are fitted with metal clasps that fit on adjacent teeth. There are times when these surrounding teeth have to be shaped to provision for the clasp fitting.
Precision Attachment Partial Denture- This denture is very different from the traditional one. The former fits right on the crown that has been affixed to your tooth and it does not have any clasps.
Valplast Partial Denture- This is a very flexible, thermo-plastic nylon, bio-compatible denture. It has very distinctive aesthetic and physical properties. It is made of a translucent material, which allows the natural color of the inner tissue to show through. This gives the dentures & partials a very natural look.
We have highly-trained and expert dentists who provide you with the best dental procedures and we also ensure that only the highest quality dentures & partials are used. The type of denture or partial that is used will depend on the condition of your natural teeth and a few other factors. We carry out a complete check-up of your teeth and analyze their condition.
We then inform you about all the alternatives and also recommend the best solutions. For the best dentures & partials, contact Brummett and Tallent Cosmetic and Family Dental on 606-340-0740 or visit us at Monticello, KY. We also have patients coming in from surrounding areas including Somerset, Danville, and Cookeville.


text:
Jun 22 - Aug 12 , 2018
Pump Boys and Dinettes
EXTENDED DUE TO POPULAR DEMAND!
"Infectiously entertaining!!" --Steven Stanley, StageScene LA
"Pump Boys and Dinettes will win you over hook, link and sinker!" - Ellen Dostal, Broadway World
-"…as close to a must see as any performance can ever be….if enjoyment is one of the major criteria for any theatrical performance then Pump Boys and Dinettes is undeniably a five star show." - Ron Irwin, Splash Magazine
"Director/choreographer Allison Bibicoff finds the right meld of sentimentality and cheeky humor ...the songs and chitchat come across as spontaneous fun, just like they should....astounding cast." - Tony Frankel, StageAndCinema.com
Get ready to stomp your feet and clap your hands for this countrified musical, the first time this Tony-nominated show has been presented in the Los Angeles area in 30 years!
Drive a ways outta town, somewhere between Frog Level and Smyrna, North Carolina and you'll come to a filling station run by L. M. and Jim. Across the blacktop is the Double Cupp Diner, operated by Rhetta and Prudie Cupp. To look at it, you wouldn't know that this little stop on Highway 57 is where all the action is, but trust us – once the boys get that guitar and bass fiddle revved up, you won't want to be anywhere else. Pump Boys and Dinettes is a countrified musical packed with highly entertaining toe-tappers such as "Drinkin' Shoes", "Farmer Tan" and "The Night Dolly Parton Was Almost Mine!"
Starring Cori Cable Kidder, the Ovation Award-nominated star of SMP's 2015 hit production Always…Patsy Cline. Kidder returns here as Rhetta Cupp, joined by Emily Kay Townsend as her sister Prudie Cupp. The Pump Boys are Sean Paxton as L.M. (musical director/keyboards) , Mike Murray as Jim (guitar), Jimmy Villaflor as Jackson(guitar), Kevin Tiernan as Eddie(bass) and Jim Miller as Bobby (drums).
Each performance, four audience members will get to sit onstage alongside the cast and musicians, and will even be treated to fresh pie! Hurry, limited spots available!
(click image for bio)
Cori Cable Kidder
Rhetta Cupp
Cori Cable Kidder is thrilled to return to Sierra Madre Playhouse following her 2017 fundraising concert Back Where I Belong and 2015 production of Always…Patsy Cline which garnered her an Ovation Best Actress in a Musical nomination for her role as Patsy Cline. Her credits include the Broadway Farewell Tour of Mamma Mia! (Donna u/s), In the Mood: A 1940s Big Band Revue, and Hello, Dolly! (Irene Malloy) in which she appeared alongside The Waltons star Judy Norton as Dolly Levi and Happy Days star Don Most as Horace Vandergelder. SMP's. Cori is also a member of the local Andrews Sisters vocal group Swing Dames. Thank you to Christian, Doug, Ward, and Estelle. To my family – thank you for encouraging me to follow this glorious dream. I love you.
www.coricablekidder.com
Michael Butler Murray*
Michael Butler Murray* is very excited to be making his SMP debut with Pump Boys and Dinettes! A veteran of the show, he performed the role of "Jackson" throughout the Netherlands as well as Stage West(Springfield, MA), The Strand Theatre (Pontiac, MI) and Traverse City, MI. Other shows include: Mamma Mia! (Harry-National Tour), I Love My Wife (Reprise!), Johnny Guitar (La Mirada), As You Like It (Goodman, Chicago), Musical! The Musical (an improvised musical - Royal George, Chicago) and Always… Patsy Cline (Apollo, Chicago). Film: Frontera, Jersey Boys. He is also the narrator of over 55 audiobooks and is one half of the guitar comedy duo, "Schoolcraft and Murray." Check out their original tunes at www.schoolcraftandmurray.com. Pump it up!
Sean Paxton
Sean Paxton (L.M., Piano & Accordian) is a composer, pianist, and musical director who returns to Sierra Madre Playhouse after writing music for Deathtrap and A Wrinkle In Time, and music directing Always…Patsy Cline and The Marvelous Wonderettes. He started his career in Los Angeles at USC and has since scored films, composed for theater, and orchestrated or arranged for everything from orchestral to pop to jazz ensembles. In the past year Sean has worked on Man of La Mancha, The Fantasticks, Sister Act, Candide, Beehive, and The Robber Bridegroom. He is a recipient of ASCAP's Harold Arlen award, and former participant in the ASCAP Film Scoring Workshop.
Emily Kay Townsend
Prudie Cupp
Emily Kay Townsend is ecstatic to be a part of Pump Boys and Dinettes. Emily, a Chicago native, started singing and playing the piano as a young girl with her father in church. She studied musical theater at AMDA College and Conservatory of the Performing Arts in NYC, obtained her Bachelor's Degree at AMDA Los Angeles, and now plays at the Actors Studio West. Some of her favorite roles include, Gretchen in Boeing-Boeing and Madeline in Hit the Wall. She would like to thank her Midwest and California family for their ongoing love and support and the community and directors at Sierra Madre Playhouse for this opportunity.
Kevin Tiernan
Kevin Tiernan Pump Boys and Dinettes is Kevin's third show at Sierra Madre Playhouse. He previously was the guitarist for Always…Patsy Cline and The Marvelous Wondrettes. In addition, he's played guitar for countless musicals at the Getty Villa, Circle X Theatre Company, The Hudson, John Anson Ford Theatre, and many others. Musicals include: Bat Boy, Bad Apples, Hair, and the West Coast premieres of Bare and Heathers - The Musical. Kevin has performed at Disney Hall with Mike Einzenger from Incubus and played guitar on the world premiere of Frank Zappa's Joe's Garage.
His film and television credits include: Lars and the Real Girl, Desperate Housewives, and Dolly Parton's Christmas of Many Colors: Circle of Love.
Jimmy Villaflor
Jimmy Villaflor is an aspiring singer-songwriter and graduate of the Thornton School of Music at the University of Southern California. He picked up guitar and began singing in his school choir at age eleven and continued his passion for music throughout high school, singing in the men's a cappella group, playing in rock bands, and performing every year in the annual variety show. All the while, Jimmy worked on honing his craft at songwriting until applying as a singer-songwriter to the Popular Music program at Thornton. Since graduating from USC, he has continued to write songs and will be releasing an album of original music this summer titled Wax & Wane. Pump Boys and Dinettes will be Jimmy's first musical theater performance.
Allison Bibicoff
Jeff Rack
Todd McCraw and Matthew Shane


text:
Why people use cannabis during pregnancy
A new, small-scale study has found that pregnant and breastfeeding people appear to be using cannabis more to manage pregnancy-related symptoms and pre-existing health conditions, including nausea, vomiting, mental health problems and insomnia, among others.
Although there is a lack of evidence on prevalence and the effects of cannabis on offspring, the research, published Monday in the Canadian Medical Association Journal (CMAJ), reports that cannabis use during pregnancy and lactation appears to be increasing.
However, the study found that the reasons why more pregnant individuals are turning to cannabis has "very little resonance" with those of recreational cannabis users.
"The reasons for use provided by our participants more closely match those identified in studies of medical cannabis use, such as for controlling pain, anxiety, depression, muscle spasms, nausea or appetite, and for sleep, with many using cannabis to manage multiple symptoms," the study's authors wrote.
The study found that this group also reported using cannabis to improve mood, mental, physical and spiritual well-being, and manage stress during some stages of pregnancy.
The study looked at 52 Canadians, of which 51 identified as women and one identified as non-binary.
The participants were at least 19 years old, had been pregnant or lactating in the past year, and had used cannabis during this time or in the three months prior to becoming pregnant.
The data was collected via interviews by phone or video call between November 2020 and March 2021. At the time of these interviews, 30 of the participants were pregnant and the remaining 22 were breastfeeding.
According to the study, researchers were able to identify three categories of reasons that people use cannabis during pregnancy and lactation: sensation seeking for fun and enjoyment; symptom management of chronic conditions and conditions related to pregnancy; and coping with the "unpleasant, but nonpathologized, experiences of life."
The reasons that participants gave for using cannabis changed throughout their pregnancy journey.
Before pregnancy, the study found that the participants reported using cannabis in these three categories in similar proportions, with many offering multiple reasons for use.
Upon learning they were pregnant, some of these individuals reported stopping cannabis use "out of fear of harm to the fetus" while others stopped because of social stigma, guilt and health reasons.
However, those who continued to use cannabis during their pregnancy reported that they were primarily doing so to manage their pregnancy symptoms, including nausea, vomiting and pain.
After birth and during lactation, reasons for cannabis use changed again and returned to resemble those expressed before pregnancy, according to the study.
While researchers say their sample was "diverse in age, geography, education and occupation," they acknowledged that it was similar to other studies of medicinal cannabis where participants were more likely to be white or Indigenous.
Researchers note that the findings may have "limited transferability" to pregnant and lactating people with other racial identities because of this.
According to researchers, the study suggests a need for counselling pregnant and lactating people on the potential harms of cannabis use, as well as the alternative approaches to symptom management.
"The dynamic nature of the reasons for use across stages speaks to participant perception of benefits and risks, and perhaps a desire to cast cannabis use during pregnancy as therapeutic because of perceived stigma," the study's authors wrote.
Dr. Meredith Vanstone, lead author and associate professor at McMaster University, said in a press release that it is important for physicians to understand why people are using cannabis during pregnancy.
"There's an opportunity here for exploring the benefits that pregnant patients are getting from cannabis and helping them find alternatives that we know are safe for both mom and baby," Vanstone said.
The study noted substitutes for cannabis can be both medical alternatives and therapeutic options.
Other studies have suggested that children who were exposed to cannabis while in the womb show higher levels of a stress hormone, anxiety, aggression, and hyperactivity. In addition, tests on the placenta indicate genetic changes linked to immune function for moms who use cannabis.
Another large study last year, led by researchers at The Ottawa Hospital, found evidence suggesting children with exposure during pregnancy had an increased risk of being diagnosed with autism. The same research team had previously reported that it also heightened the risk of early labour and has been linked to low birth weight.
Tags: Cannabis, People, pregnancy
Doctors Surgeries Refuse to Admit Non-Vaccinated Patients
U.S IVF Services Market Projected To Display A Robust Growth With a CAGR of 6.8% by 2028 – mainlander.nz


The idea was to bring together a group of remarkable people to see if they could become something more. To see if they could work together when we needed them to fight the battles we never could. Unfortunately though, after the falling out of Captain America: Civil War, it seems that everyone had better things to do, with the new Captain Marvel Prelude comic showing Nick Fury and Maria Hill trying and failing to bring the old gang back together.
Rumor: Is This the Superhero Lineup for 'Avengers: Infinity War'?
The Hunt For Crossbones – What Happens Between Winter Soldier And Civil War?