The eighth moment of the Riemann zeta function

In this article, we establish an asymptotic formula for the eighth moment of the Riemann zeta function, assuming the Riemann hypothesis and a quaternary additive divisor conjecture. This builds on the work of the first author on the sixth moment of the Riemann zeta function and work of Conrey-Gonek...

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Bibliographic Details
Published inarXiv.org
Main Authors Ng, Nathan, Shen, Quanli, Peng-Jie, Wong
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 29.04.2022
Subjects
Hypotheses
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Summary:In this article, we establish an asymptotic formula for the eighth moment of the Riemann zeta function, assuming the Riemann hypothesis and a quaternary additive divisor conjecture. This builds on the work of the first author on the sixth moment of the Riemann zeta function and work of Conrey-Gonek and Ivi\'{c}. A key input is a sharp bound for a certain shifted moment of the Riemann zeta function, assuming the Riemann hypothesis.
ISSN:2331-8422