Explicit extreme values of the argument of the Riemann zeta-function

Abstract We investigate explicit extreme values of the argument of the Riemann zeta-function in short intervals. As an application, we improve the result of Conrey and Turnage–Butterbaugh concerning r -gaps between zeros of the Riemann zeta-function.

Authors

Shōta Inoue (ORCID: https://orcid.org/0000-0002-0731-4008)
Yuichiro Toma (ORCID: https://orcid.org/0000-0001-9620-1007)
HIROTAKA KOBAYASHI

Institutions

Nihon University (JP)
Waseda University (JP)
National Fisheries University (JP)

Publication Details

Journal: Mathematical Proceedings of the Cambridge Philosophical Society
Published: 2026-05-29
DOI: https://doi.org/10.1017/s0305004126102060
Primary Topic: Analytic Number Theory Research
Type: article
Field-Weighted Citation Impact: 0.00

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article

Explicit extreme values of the argument of the Riemann zeta-function

Shōta Inoue, Yuichiro Toma, HIROTAKA KOBAYASHI

May 29, 2026

Mathematical Proceedings of the Cambridge Philosophical Society

Analytic Number Theory Research

article

Explicit extreme values of the argument of the Riemann zeta-function

Shōta Inoue, Yuichiro Toma, HIROTAKA KOBAYASHI

May 29, 2026article en

Abstract

Abstract We investigate explicit extreme values of the argument of the Riemann zeta-function in short intervals. As an application, we improve the result of Conrey and Turnage–Butterbaugh concerning r -gaps between zeros of the Riemann zeta-function.

Mathematical Proceedings of the Cambridge Philosophical Society

Nihon University (JP), Waseda University (JP), National Fisheries University (JP)

Reduced inequalities

Openalex Percentile: Top 3%

Analytic Number Theory Research

DOI Source OpenAlex

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