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)
Affiliation
External organisation
DOI related publication
https://doi.org/10.1016/j.aim.2019.106926
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https://resolver.tudelft.nl/uuid:da3423fd-a776-4eef-b18f-2ccd13dfae0d
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Publication Year
2020
Language
English
Affiliation
External organisation
Volume number
361
Pages (from-to)
1-22
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.
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