The second moment of the Riemann zeta function at its local extrema

IF 1.2 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series Pub Date : 2025-07-29 DOI:10.1112/jlms.70250

Christopher Hughes, Solomon Lugmayer, Andrew Pearce-Crump

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Abstract

Conrey and Ghosh studied the second moment of the Riemann zeta function, evaluated at its local extrema along the critical line, finding the leading order behaviour to be $\frac{e^{2} - 5}{2 π} T {(\log T)}^{2}$ . This problem is closely related to a mixed moment of the Riemann zeta function and its derivative. We present a new approach which will uncover the lower order terms for the second moment as a descending chain of powers of logarithms in the asymptotic expansion.

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黎曼函数在局部极值处的二阶矩

Conrey和Ghosh研究了Riemann zeta函数的第二矩，在其沿临界线的局部极值处求值，发现阶行为为e 2−5 2 π T (logt (2) $\frac{e^2 - 5}{2 \pi } T (\log T)^2$。这个问题与黎曼ζ函数及其导数的混合矩密切相关。我们提出了一种新的方法，它将揭示第二矩的低阶项在渐近展开中作为对数幂次的下降链。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of the London Mathematical Society-Second Series 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

186

审稿时长

6-12 weeks

期刊介绍： The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.