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Pair correlation estimates for the zeros of the zeta function via semidefinite programming. / Chirre, Andrés ; Goncalves, Felipe; de Laat, David.

In: Advances in Mathematics, Vol. 361, 106926, 12.02.2020, p. 1-22.

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Chirre, Andrés ; Goncalves, Felipe ; de Laat, David. / Pair correlation estimates for the zeros of the zeta function via semidefinite programming. In: Advances in Mathematics. 2020 ; Vol. 361. pp. 1-22.

BibTeX

@article{da3423fda7764eefb18f2ccd13dfae0d,
title = "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 (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.",
keywords = "Pair correlation, Semidefinite programming, Zeta function, Zeta zeros",
author = "Andr{\'e}s Chirre and Felipe Goncalves and {de Laat}, David",
year = "2020",
month = feb,
day = "12",
doi = "10.1016/j.aim.2019.106926",
language = "English",
volume = "361",
pages = "1--22",
journal = "Advances in Mathematics",
issn = "0001-8708",
publisher = "Academic Press",

}

RIS

TY - JOUR

T1 - Pair correlation estimates for the zeros of the zeta function via semidefinite programming

AU - Chirre, Andrés

AU - Goncalves, Felipe

AU - de Laat, David

PY - 2020/2/12

Y1 - 2020/2/12

N2 - 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.

AB - 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.

KW - Pair correlation

KW - Semidefinite programming

KW - Zeta function

KW - Zeta zeros

UR - http://www.scopus.com/inward/record.url?scp=85075627354&partnerID=8YFLogxK

U2 - 10.1016/j.aim.2019.106926

DO - 10.1016/j.aim.2019.106926

M3 - Article

VL - 361

SP - 1

EP - 22

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

M1 - 106926

ER -

ID: 68566512