Pair Correlation Estimates for the Zeros of the Zeta Function via\n Semidefinite Programming

2018/10/20 by Andrés Chirre, Chirre, Andrés, Felipe Gonçalves +3 · 2 citations
Mathematics · #11M26 #90C22 #Advanced Mathematical Identities #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Inequalities and Applications #Number Theory (math.NT) #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1810.08843

openalex publication_date 2018/10/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study the distribution of the non-trivial zeros of the\nRiemann zeta-function \ζ(s) (and other L-functions) using Montgomery's\npair correlation approach. We use semidefinite programming to improve upon\nnumerous asymptotic bounds in the theory of \ζ(s), including the\nproportion of distinct zeros, counts of small gaps between zeros, and sums\ninvolving multiplicities of zeros.\n

Cited by

• Zeta Zeros on the Critical Line
• The Alternative Hypothesis for Zeros of the Riemann Zeta-Function

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