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

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

Journal Article (2020)

Author(s)

Andrés Chirre (Instituto Nacional de Matemática Pura e Aplicada - IMPA)

Felipe Goncalves (Universität Bonn)

David de Laat (Massachusetts Institute of Technology)

Semidefinite programming Pair correlation Zeta function Zeta zeros

DOI related publication

https://doi.org/10.1016/j.aim.2019.106926 Final published version

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https://resolver.tudelft.nl/uuid:da3423fd-a776-4eef-b18f-2ccd13dfae0d

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Publication Year

2020

Language

English

Journal title

Advances in Mathematics

Volume number

361

Article number

106926

Pages (from-to)

1-22

Downloads counter

237

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.