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

Journal article (2020)

Authors

Andrés Chirre Instituto Nacional de Matemática Pura e Aplicada - IMPA
Felipe Goncalves Universität Bonn
D. de Laat Massachusetts Institute of Technology
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Published Date

12-02-2020

Language

English

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Abstract

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