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

Shōta Inoue; HIROTAKA KOBAYASHI; Yuichiro Toma

doi:10.1017/s0305004126102060

May 29, 2026Mathematical Proceedings of the Cambridge Philosophical Society

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

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Key Points

This research aims to explore explicit extreme values of the Riemann zeta-function's argument in specific intervals and improve existing results regarding gaps between its zeros.
Analyzed extreme values of the Riemann zeta-function's argument over short intervals.
Built upon prior work by Conrey and Turnage–Butterbaugh on r-gaps between zeros.
Improved understanding of the r-gaps between zeros of the Riemann zeta-function.
Demonstrated more precise extreme values of the argument.

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Implication

Investigates extreme values of the Riemann zeta-function's argument, enhancing understanding of gaps between zeros.

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.

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Inoue et al. (2026) studied this question.

synapsesocial.com/papers/6a1bd0b55783ba022b6fc604 https://doi.org/10.1017/s0305004126102060

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

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Abstract

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

Key Points

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Implication

Abstract

Discussion

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