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Maximum of the Riemann zeta function on a short interval of the critical line

Arguin, Louis-Pierre and Belius, David and Bourgade, Paul and Radziwiłł, Maksym and Soundararajan, Kannan (2016) Maximum of the Riemann zeta function on a short interval of the critical line. . (Submitted) https://resolver.caltech.edu/CaltechAUTHORS:20180612-140618985

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Abstract

We prove the leading order of a conjecture by Fyodorov, Hiary and Keating, about the maximum of the Riemann zeta function on random intervals along the critical line. More precisely, as T→∞ for a set of t∈[T,2T] of measure (1−o(1))T, we have max|t−u|≤1log∣∣ζ(12+iu)∣∣=(1+o(1))loglogT.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
https://arxiv.org/abs/1612.08575arXivDiscussion Paper
Record Number:CaltechAUTHORS:20180612-140618985
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20180612-140618985
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:87019
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:12 Jun 2018 21:13
Last Modified:03 Oct 2019 19:51

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