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

Andrés Chirre, Felipe Goncalves, David de Laat

Research output: Contribution to journalArticleScientificpeer-review

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.
Original languageEnglish
Article number106926
Pages (from-to)1-22
Number of pages22
JournalAdvances in Mathematics
Volume361
DOIs
Publication statusPublished - 12 Feb 2020
Externally publishedYes

Keywords

  • Pair correlation
  • Semidefinite programming
  • Zeta function
  • Zeta zeros

Fingerprint Dive into the research topics of 'Pair correlation estimates for the zeros of the zeta function via semidefinite programming'. Together they form a unique fingerprint.

Cite this