Unconditional lower bounds for the sixth and eighth moments of the Riemann zeta function

IF 0.7 3区数学 Q3 MATHEMATICS

Journal of Number Theory Pub Date : 2025-09-23 DOI:10.1016/j.jnt.2025.08.017

Timothy Page

引用次数: 0

Abstract

Unconditional bounds on the sixth and eighth moments of the Riemann zeta function are improved by bounding twisted second and fourth moments that arise upon application of the Cauchy-Schwarz inequality and Hölder's inequality. An unconditional bound on the sixth moment of the derivative of the Riemann zeta function is also deduced.

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黎曼函数的第六阶矩和第八阶矩的无条件下界

利用Cauchy-Schwarz不等式和Hölder不等式，对Riemann zeta函数的第6和第8矩的无条件界进行了改进。推导出黎曼ζ函数导数的第六阶矩的无条件界。

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 Number Theory 数学-数学

CiteScore

1.30

自引率

14.30%

发文量

122

审稿时长

16 weeks

期刊介绍： The Journal of Number Theory (JNT) features selected research articles that represent the broad spectrum of interest in contemporary number theory and allied areas. A valuable resource for mathematicians, the journal provides an international forum for the publication of original research in this field. The Journal of Number Theory is encouraging submissions of quality, long articles where most or all of the technical details are included. The journal now considers and welcomes also papers in Computational Number Theory. Starting in May 2019, JNT will have a new format with 3 sections: JNT Prime targets (possibly very long with complete proofs) high impact papers. Articles published in this section will be granted 1 year promotional open access. JNT General Section is for shorter papers. We particularly encourage submission from junior researchers. Every attempt will be made to expedite the review process for such submissions. Computational JNT . This section aims to provide a forum to disseminate contributions which make significant use of computer calculations to derive novel number theoretic results. There will be an online repository where supplementary codes and data can be stored.