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Published December 2019 | Submitted
Journal Article Open

Sharp Upper Bounds for Fractional Moments of the Riemann Zeta Function


We establish sharp upper bounds for the 2kth moment of the Riemann zeta function on the critical line, for all real 0 ⩽ k ⩽ 2⁠. This improves on earlier work of Ramachandra, Heath-Brown and Bettin–Chandee–Radziwiłł.

Additional Information

© The author(s) 2019. Published by Oxford University Press. This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model). Received: 05 February 2019; Accepted: 03 June 2019; Published: 26 September 2019. The first author is supported by European Research Council grant no. 670239. The second author acknowledges the support of a Sloan fellowship. The third author is partially supported by a grant from the National Science Foundation, and by a Simons Investigator grant from the Simons Foundation.

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August 19, 2023
October 19, 2023