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

被引：53

作者：

Arguin, Louis-Pierre ^{[1
,6
]}

Belius, David ^{[2
]}

Bourgade, Paul ^{[3
]}

Radziwill, Maksym ^{[4
]}

Soundararajan, Kannan ^{[5
]}

机构：

[1] CUNY, Baruch Coll, Grad Ctr, New York, NY 10021 USA

[2] Univ Zurich, Inst Math, Winterthurerstr 190, CH-8057 Zurich, Switzerland

[3] Courant Inst, 251 Mercer St,Room 603, New York, NY 10012 USA

[4] McGill Univ, Dept Math, 805 Sherbrooke St, West Montreal, PQ H3A 0G4, Canada

[5] Stanford Univ, 450 Serra Mall,Bldg 380, Stanford, CA 94305 USA

[6] Baruch Coll, One Bernard Baruch Way, New York, NY 10010 USA

来源：

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS | 2019年 / 72卷 / 03期

基金：

美国国家科学基金会; 加拿大自然科学与工程研究理事会;

关键词：

EXTREME VALUES;

D O I：

10.1002/cpa.21791

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 -> infinity for a set of t SMALL ELEMENT OF [T, 2T] of measure (1-o(1)) T, we have max(vertical bar t-u vertical bar <= 1)log|zeta(1/2+iu)vertical bar=(1+o(1))loglogT. (c) 2018 Wiley Periodicals, Inc.

引用

页码：500 / 535

页数：36

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