黎曼ζ函数在临界线上的平方的相关性

IF 1.2 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series Pub Date : 2025-09-14 DOI:10.1112/jlms.70289

Valeriya Kovaleva

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引用次数: 0

摘要

我们计算了Riemann zeta函数的两个移位平方乘积在临界线上的平均值，其移位的大小可达T³/2- ε $T^{3/2-\varepsilon}$。我们给出了这种平均值的显式表达式，并推导了误差项的近似谱展开，类似于Motohashi的。因此，我们还计算了Riemann zeta函数的(2,2)-矩，为此我们部分验证（并部分驳斥）了Bailey和Keating的一个猜想。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Correlations of the squares of the Riemann zeta function on the critical line

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Correlations of the squares of the Riemann zeta function on the critical line

We compute the average of a product of two shifted squares of the Riemann zeta function on the critical line with shifts up to size $T^{3 / 2 - ε}$ . We give an explicit expression for such an average and derive an approximate spectral expansion for the error term similar to Motohashi's. As a consequence, we also compute the (2,2)-moment of moment of the Riemann zeta function, for which we partially verify (and partially refute) a conjecture of Bailey and Keating.

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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.