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arXiv · 2204.13891

The eighth moment of the Riemann zeta function

Nathan Ng·Quanli Shen·Peng-Jie Wong
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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.

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Nathan Ng, Quanli Shen, Peng-Jie Wong. 2022-04-29. The eighth moment of the Riemann zeta function. https://arxiv.org/abs/2204.13891

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