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

共 50 条

[31] AN ASYMPTOTIC REPRESENTATION FOR THE RIEMANN ZETA-FUNCTION ON THE CRITICAL LINE
PARIS, RB
PROCEEDINGS OF THE ROYAL SOCIETY-MATHEMATICAL AND PHYSICAL SCIENCES, 1994, 446 (1928): : 565 - 587
[32] a-Points of the Riemann Zeta-Function on the Critical Line
Lester, Stephen J.
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2015, 2015 (09) : 2406 - 2436
[33] ON THE MEANS OF THE ARGUMENT OF THE RIEMANN ZETA-FUNCTION ON THE CRITICAL LINE
GROENEWALD, L
ACTA MATHEMATICA HUNGARICA, 1991, 58 (1-2) : 25 - 29
[34] Weighted value distributions of the Riemann zeta function on the critical line
Fazzari, Alessandro
FORUM MATHEMATICUM, 2021, 33 (03) : 579 - 592
[35] ON THE NUMBER OF ZEROS OF THE RIEMANN ZETA-FUNCTION LYING IN ALMOST ALL SHORT INTERVALS OF THE CRITICAL LINE
KARATSUBA, AA
RUSSIAN ACADEMY OF SCIENCES IZVESTIYA MATHEMATICS, 1993, 40 (02): : 353 - 376
[36] Is the Riemann Zeta Function in a Short Interval a 1-RSB Spin Glass?
Arguin, Louis-Pierre
Tai, Warren
SOJOURNS IN PROBABILITY THEORY AND STATISTICAL PHYSICS - I: SPIN GLASSES AND STATISTICAL MECHANICS, A FESTSCHRIFT FOR CHARLES M. NEWMAN, 2019, 298 : 63 - 88
[37] AT LEAST 2/5 OF THE ZEROS OF THE RIEMANN ZETA FUNCTION ARE ON THE CRITICAL LINE
CONREY, JB
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1989, 20 (01) : 79 - 81
[38] THE RIEMANN ZETA FUNCTION AND GAUSSIAN MULTIPLICATIVE CHAOS: STATISTICS ON THE CRITICAL LINE
Saksman, Eero
Webb, Christian
ANNALS OF PROBABILITY, 2020, 48 (06): : 2680 - 2754
[39] A note on the zeros of the derivative of the Riemann zeta function near the critical line
Feng, SJ
ACTA ARITHMETICA, 2005, 120 (01) : 59 - 68
[40] On the extreme values of the Riemann zeta function on random intervals of the critical line
Joseph Najnudel
Probability Theory and Related Fields, 2018, 172 : 387 - 452

← 1 2 3 4 5 →