Pair Correlation estimates for the zeros of the zeta function via semidefinite programming

Abstract

In this paper we study the distribution of the non-trivial zeros of the Riemann zeta-function ζ(s) (and other L-functions) using Montgomery's pair correlation approach. We use semidefinite programming to improve upon numerous asymptotic bounds in the theory of ζ(s), including the proportion of distinct zeros, counts of small gaps between zeros, and sums involving multiplicities of zeros.