Random matrices and L-functions

被引:55
作者
Keating, JP [1 ]
Snaith, NC [1 ]
机构
[1] Univ Bristol, Sch Math, Bristol BS8 1TW, Avon, England
来源
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL | 2003年 / 36卷 / 12期
关键词
D O I
10.1088/0305-4470/36/12/301
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
In recent years there has been a growing interest in connections between the statistical properties of number theoretical L-functions and random matrix theory. We review the history of these connections, some of the major achievements and a number of applications.
引用
收藏
页码:2859 / 2881
页数:23
相关论文
共 64 条
[41]   Random matrix theory and discrete moments of the Riemann zeta function [J].
Hughes, CP .
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2003, 36 (12) :2907-2917
[42]   On the characteristic polynomial of a random unitary matrix [J].
Hughes, CP ;
Keating, JP ;
O'Connell, N .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2001, 220 (02) :429-451
[43]  
HUGHES CP, 2002, MATHNT0208230
[44]  
Ingham A. E., 1926, P LOND MATH SOC, Vs2-27, P273, DOI [10.1112/plms/s2-27.1.273, DOI 10.1007/S40687-020-00234-3]
[45]  
IVIC A, 1991, MEAN VALUES RIEMANN
[46]  
Jutila M., 1981, ANALYSIS, V1, P149
[47]  
Katz N., 1999, RANDOM MATRICES FROB
[48]   Zeroes of zeta functions and symmetry [J].
Katz, NM ;
Sarnak, P .
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1999, 36 (01) :1-26
[49]  
KEATING J, 1993, P INT SCH PHYS, V119, P145
[50]  
Keating J P, 1999, SUPERSYMMETRY TRACE, P1