TY - JOUR

T1 - Maximum of the Riemann Zeta Function on a Short Interval of the Critical Line

AU - Arguin, Louis Pierre

AU - Belius, David

AU - Bourgade, Paul

AU - Radziwiłł, Maksym

AU - Soundararajan, Kannan

N1 - Funding Information:
Acknowledgment. The authors thank the referee for useful comments that led to an improvement of the first version of this paper. L.-P. A. is supported by National Science Foundation CAREER 1653602, National Science Foundation Grant DMS-1513441, and a Eugene M. Lang Junior Faculty Research Fellowship. D. B. is grateful for the hospitality of the Courant Institute during visits where part of this work was carried out. P. B. is supported by National Science Foundation Grant DMS-1513587. M. R. is supported by an NSERC DG grant, the CRC program, and a Sloan Fellowship. K. S. is partly supported by a grant from the National Science Foundation and a Simons Investigator grant from the Simons Foundation.
Publisher Copyright:
© 2018 Wiley Periodicals, Inc.

PY - 2019/3

Y1 - 2019/3

N2 - 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 (Formula presented.)

AB - 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 (Formula presented.)

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U2 - 10.1002/cpa.21791

DO - 10.1002/cpa.21791

M3 - Article

AN - SCOPUS:85053428438

VL - 72

SP - 500

EP - 535

JO - Communications on Pure and Applied Mathematics

JF - Communications on Pure and Applied Mathematics

SN - 0010-3640

IS - 3

ER -