The eighth moment of the Riemann zeta function

2022/04/29 by Nathan Ng, Ng, Nathan, Quanli Shen +3 · 1 citation
Mathematics · #Analytic Number Theory Research #Meromorphic and Entire Functions #Advanced Mathematical Identities

paper · pdf · doi:10.48550/arxiv.2204.13891

Abstract

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 Ivić. A key input is a sharp bound for a certain shifted moment of the Riemann zeta function, assuming the Riemann hypothesis.

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• Continuation of Dirichlet series I

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