JournalsjemsVol. 28, No. 10pp. 4175–4237

The eighth moment of the Riemann zeta function

  • Nathan Ng

    University of Lethbridge, Canada

  • Quanli Shen

    Shandong University, Weihai, P. R. China

  • Peng-Jie Wong

    National Sun Yat-Sen University, Kaohsiung City, Taiwan
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Abstract

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 the works 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.

Cite this article

Nathan Ng, Quanli Shen, Peng-Jie Wong, The eighth moment of the Riemann zeta function. J. Eur. Math. Soc. 28 (2026), no. 10, pp. 4175–4237

DOI 10.4171/JEMS/1568