A note on r-gaps between zeros of the Riemann zeta-function

2023/03/12 by Shōta Inoue, Inoue, Shōta · 1 citation
Mathematics · #11M06 #11M26 #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2303.06613

openalex publication_date 2023/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we prove Selberg's announced result on r-gaps between zeros of the Riemann zeta-function ζ. Our proof uses a result on variations of argζ by Tsang based on Selberg's method. The same result with explicit constants under the Riemann Hypothesis has been obtained by Conrey and Turnage-Butterbaugh using a different method. We explain how to obtain explicit constants under the Riemann Hypothesis using our approach which is based on Selberg's and Tsang's arguments.

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