An Exact Formula for the Prime Counting Function
This article will discuss a few main topics in Number Theory, such as the Mobius function and its generalization, leading up to the derivation of a neat power series for the prime counting function, \pi(x) Among its main findings, we can cite the inversion theorem for Dirichlet series (given $F_a(s) we can tell what its associated function, $a(n) is) which enabled the creation of a formula for \pi(x) in the first place, and the realization that sums of divisors and the Mobius function are particular cases of a more general concept. Another conclusion we draw is that it's unnecessary to resort to the zeros of the analytic continuation of the zeta function to obtain \pi(x)