  Recently in joint work with E. Sert, we proved sharp boundedness results on
discrete fractional integral operators along binary quadratic forms. Present
work vastly enhances the scope of those results by extending boundedness to
bivariate quadratic polynomials. We achieve this in part by establishing
connections to problems on concentration of lattice points on short arcs of
conics, whence we study discrete fractional integrals and lattice point
concentration from a unified perspective via tools of sieving and diophantine
approximation, and prove theorems that are of interest to researchers in both
subjects.

Classical Analysis and ODEs;Number Theory