Random matrix theory and discrete moments of the Riemann zeta function

被引：14

作者：

Hughes, CP ^{[1
]}

机构：

[1] Tel Aviv Univ, Raymond & Beverly Sackler Fac Exact Sci, IL-69978 Tel Aviv, Israel

来源：

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL | 2003年 / 36卷 / 12期

关键词：

D O I：

10.1088/0305-4470/36/12/303

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We calculate the discrete moments of the characteristic polynomial of a random unitary matrix, evaluated a small distance away from an eigenangle. Such results allow us to make conjectures about similar moments for the Riemann zeta function, and provide a uniform approach to understanding moments of the zeta function and its derivative.

引用

页码：2907 / 2917

页数：11

共 18 条

[1]

Abramowitz M., 1972, HDB MATH FUNCTIONS 9

[2] ASYMPTOTIC FORMULAS FOR TOEPLITZ DETERMINANTS [J].

BASOR, E .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1978, 239 (MAY) :33-65

[3] LARGE GAPS BETWEEN ZEROS OF THE ZETA-FUNCTION [J].

CONREY, JB ;

GHOSH, A ;

GONEK, SM .

MATHEMATIKA, 1986, 33 (66) :212-238

[4]

Conrey JB, 1998, INT MATH RES NOTICES, V1998, P775

[5] High moments of the Riemann zeta-function [J].

Conrey, JB ;

Gonek, SM .

DUKE MATHEMATICAL JOURNAL, 2001, 107 (03) :577-604

[6] SELBERG CORRELATION INTEGRALS AND THE 1/R2 QUANTUM MANY-BODY SYSTEM [J].

FORRESTER, PJ .

NUCLEAR PHYSICS B, 1992, 388 (03) :671-699

[7] ON NEGATIVE MOMENTS OF THE RIEMANN ZETA-FUNCTION [J].

GONEK, SM .

MATHEMATIKA, 1989, 36 (71) :71-88

[8] MEAN-VALUES OF THE RIEMANN ZETA-FUNCTION AND ITS DERIVATIVES [J].

GONEK, SM .

INVENTIONES MATHEMATICAE, 1984, 75 (01) :123-141

[9]

Hardy GH, 1918, ACTA MATH-DJURSHOLM, V41, P119

[10] Random matrix theory and the derivative of the Riemann zeta function [J].

Hughes, CP ;

Keating, JP ;

O'Connell, N .

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2000, 456 (2003) :2611-2627

← 1 2 →