On the mean values of dirichlet l-functions

被引：16

作者：

Bui, H. M. ^{[1
]}

Keating, J. P. ^{[1
]}

机构：

[1] Univ Bristol, Sch Math, Bristol BS8 1TW, Avon, England

来源：

PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY | 2007年 / 95卷

基金：

英国工程与自然科学研究理事会;

关键词：

D O I：

10.1112/plms/pdm008

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the 2kth power moment of Dirichlet L-functions L(s, chi) at the centre of the critical strip (s = 1/2), where the average is over all primitive characters chi (mod q). We extend to this case the hybrid Euler-Hadamard product results of Gonek, Hughes and Keating for the Riemann zeta function. This allows us to recover conjectures for the moments based on random matrix models, incorporating the arithmetical terms in a natural way.

引用

页码：273 / 298

页数：26

共 11 条

[1] On the distribution of zeros of linear combinations of Euler products
Bombieri, E
Hejhal, DA
[J]. DUKE MATHEMATICAL JOURNAL, 1995, 80 (03) : 821 - 862
[2] Integral moments of L-functions
Conrey, JB
Farmer, DW
Keating, JP
Rubinstein, MO
Snaith, NC
[J]. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 2005, 91 : 33 - 104
[3] Conrey JB, 2000, INT MATH RES NOTICES, V2000, P883
[4] Gonek SM, 2007, DUKE MATH J, V136, P507
[5] Heath-Brown D.R., 1981, Analysis, V1, P25
[6] HEATHBROWN DR, 1979, P LOND MATH SOC, V38, P385
[7] Random Matrix Theory and ζ(1/2+it)
Keating, JP
Snaith, NC
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2000, 214 (01) : 57 - 89
[8] Random matrix theory and L-functions at s=1/2
Keating, JP
Snaith, NC
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2000, 214 (01) : 91 - 110
[9] Paley REAC, 1931, P LOND MATH SOC, V32, P273
[10] SHIU P, 1980, J REINE ANGEW MATH, V313, P161

← 1 2 →