Pair Correlation of zeros of Dirichlet L-Functions: A possible path towards the conjectures of Chowla, Elliott-Halberstam and Montgomery

Assuming the Generalized Riemann Hypothesis and a pair correlation conjecture for the zeros of Dirichlet L-functions, we establish the truth of a conjecture of Montgomery (in its corrected form stated by Friedlander and Granville) on the magnitude of the error term in the prime number theorem in arithmetic progressions. As a consequence, we obtain that, under the same assumptions, the Elliott--Halberstam conjecture holds true. As another consequence, under the same assumptions, we will show that the number of Dirichlet characters chi mod q for which L(1/2,chi) =0 is of order less than q^{1/2+epsilon}.