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

Shōta Inoue

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arXiv · 2303.06613

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

Shōta Inoue

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Abstract

In this note, we prove Selberg's announced result on $r$-gaps between zeros of the Riemann zeta-function $\zeta$. Our proof uses a result on variations of $\arg\zeta$ 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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Shōta Inoue. 2023-03-12. A note on $r$-gaps between zeros of the Riemann zeta-function. https://arxiv.org/abs/2303.06613

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