The eighth moment of the Riemann zeta function

TL;DR

This paper derives an asymptotic formula for the eighth moment of the Riemann zeta function under the Riemann hypothesis and a divisor conjecture, extending previous work on lower moments.

Contribution

It provides the first asymptotic formula for the eighth moment of the Riemann zeta function assuming key conjectures, advancing understanding of high moments.

Findings

Established asymptotic formula for the eighth moment

Provided a sharp bound for a shifted moment of zeta

Extended methods from sixth to eighth moment analysis

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 Ivi\'{c}. A key input is a sharp bound for a certain shifted moment of the Riemann zeta function, assuming the Riemann hypothesis.