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Sharp Upper Bounds for Fractional Moments of the Riemann Zeta Function

Heap, Winston and Radziwiłł, Maksym and Soundararajan, K. (2019) Sharp Upper Bounds for Fractional Moments of the Riemann Zeta Function. Quarterly Journal of Mathematics, 70 (4). pp. 1387-1396. ISSN 0033-5606.

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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.

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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 ( 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.
Funding AgencyGrant Number
European Research Council (ERC)670239
Alfred P. Sloan FoundationUNSPECIFIED
Simons FoundationUNSPECIFIED
Issue or Number:4
Record Number:CaltechAUTHORS:20200213-072834344
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Official Citation:Winston Heap, Maksym Radziwiłł, K Soundararajan, Sharp Upper Bounds for Fractional Moments of the Riemann Zeta Function, The Quarterly Journal of Mathematics, Volume 70, Issue 4, December 2019, Pages 1387–1396,
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:101259
Deposited By: Tony Diaz
Deposited On:13 Feb 2020 15:35
Last Modified:13 Feb 2020 15:35

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