Sharp Upper Bounds for Fractional Moments of the Riemann Zeta Function

Creators: Heap, Winston; Radziwiłł, Maksym; Soundararajan, K.

Abstract

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.

Attached Files

Submitted - 1901.08423.pdf

Files

1901.08423.pdf

Files (156.5 kB)

Name	Size	Download all
1901.08423.pdf md5:982dd864f8e4aca38b7899bc883c075a	156.5 kB	Preview Download

Additional details

	All versions	This version
Views	0	0
Downloads	0	0
Data volume	0 Bytes	0 Bytes