黎曼函数在局部极值处的二阶矩

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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引用次数: 0

摘要

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。

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

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

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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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.