A survey of moment bounds for ζ(s): From Heath‐Brown's work to the present
Abstract
Abstract In this expository article, we review some of the ideas behind the work of Heath–Brown (D. R. Heath‐Brown, J. London Math. Soc., (2), 24 , (1981), no. 1, 65–78) on upper and lower bounds for moments of the Riemann zeta‐function, as well as the impact this work had on subsequent developments in the field. We survey recent results on the topic, which essentially recover the expected rate of growth for all moments — unconditionally for small moments and conditionally on the Riemann hypothesis for all larger moments.
Fields of Study & Subjects
Analytic Number Theory Research
Meromorphic and Entire Functions
Advanced Mathematical Identities
Publication details
- Journal / source
- Journal of the London Mathematical Society
- Volume
- 113
- Issue
- 1
- Publication date
- 1 January 2026
- Language
- EN