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

被引：54

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 39 条

[1] Arguin L.-P., 2017, ADV DISORDERED SYSTE, P166
[2] MAXIMA OF A RANDOMIZED RIEMANN ZETA FUNCTION, AND BRANCHING RANDOM WALKS
Arguin, Louis-Pierre
Belius, David
Harper, Adam J.
[J]. ANNALS OF APPLIED PROBABILITY, 2017, 27 (01) : 178 - 215
[3] Maximum of the Characteristic Polynomial of Random Unitary Matrices
Arguin, Louis-Pierre
Belius, David
Bourgade, Paul
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2017, 349 (02) : 703 - 751
[4] FREQUENCY OF TITCHMARSHS PHENOMENON FOR ZETA(S) .3.
BALASUBRAMANIAN, R
RAMACHANDRA, K
[J]. PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES SECTION A, 1977, 86 (04): : 341 - 351
[5] New Computations of the Riemann Zeta Function on the Critical Line
Bober, Jonathan W.
Hiary, Ghaith A.
[J]. EXPERIMENTAL MATHEMATICS, 2018, 27 (02) : 125 - 137
[6] LARGE GREATEST COMMON DIVISOR SUMS AND EXTREME VALUES OF THE RIEMANN ZETA FUNCTION
Bondarenko, Andriy
Seip, Kristian
[J]. DUKE MATHEMATICAL JOURNAL, 2017, 166 (09) : 1685 - 1701
[7] Mesoscopic fluctuations of the zeta zeros
Bourgade, P.
[J]. PROBABILITY THEORY AND RELATED FIELDS, 2010, 148 (3-4) : 479 - 500
[8] DECOUPLING, EXPONENTIAL SUMS AND THE RIEMANN ZETA FUNCTION
Bourgain, J.
[J]. JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2017, 30 (01) : 205 - 224
[9] MAXIMAL DISPLACEMENT OF BRANCHING BROWNIAN-MOTION
BRAMSON, MD
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1978, 31 (05) : 531 - 581
[10] Bounding |ζ(1/2+it)| on the Riemann hypothesis
Chandee, Vorrapan
Soundararajan, K.
[J]. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2011, 43 : 243 - 250

← 1 2 3 4 →