关于黎曼zeta函数零点间r $r$ 缺口的说明

IF 0.8 3区数学 Q2 MATHEMATICS Bulletin of the London Mathematical Society Pub Date : 2024-04-27 DOI:10.1112/blms.13054

Shōta Inoue

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摘要

在本文中，我们证明了塞尔伯格宣布的关于黎曼zeta函数ζ $\zeta$ 的零点间r $r$ -间隙的结果。我们的证明使用了曾氏基于塞尔伯格方法的 arg ζ $\arg \zeta$ 变化结果。康雷（Conrey）和特纳吉-巴特鲍（Turnage-Butterbaugh）用不同的方法得到了黎曼假说下具有显式常数的相同结果。我们将解释如何根据塞尔伯格和曾氏的论证，用我们的方法得到黎曼假设下的显式常数。

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

In this paper, 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 $arg ζ$ 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.