EXPLICIT FORMULAE FOR THE MEAN VALUE OF PRODUCTS OF VALUES OF DIRICHLET L-FUNCTIONS AT POSITIVE INTEGERS

被引：0

作者：

Louboutin, Stephane R. ^{[1
]}

机构：

[1] Aix Marseille Univ, CNRS, Cent Marseille, I2M, Marseille, France

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2024年 / 152卷 / 11期

关键词：

Dirichlet L-functions; characters; cotangent; mean value;

D O I：

10.1090/proc/16960

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let m >= 1 be a rational integer. We give an explicit formula for the mean value 2/phi(f) Sigma(chi(-1)=(-1)m) vertical bar L(m, chi)vertical bar(2), where chi ranges over the phi(f)/2 Dirichlet characters modulo f > 2 with the same parity as m. We then adapt our proof to obtain explicit means values for products of the form L(m(1), chi(1)) ... L(m(n-1,) chi(n-1))<(L(m(n), chi(1) ... chi(n-1)))over bar>.

引用

页码：4623 / 4631

页数：9

共 50 条

[31] AN IMPROVED UPPER BOUND FOR THE ERROR IN THE ZERO-COUNTING FORMULAE FOR DIRICHLET L-FUNCTIONS AND DEDEKIND ZETA-FUNCTIONS
Trudgian, T. S.
[J]. MATHEMATICS OF COMPUTATION, 2015, 84 (293) : 1439 - 1450
[32] On asymptotic properties of the generalized Dirichlet L-functions
Ma, Rong
Niu, Yana
Zhang, Yulong
[J]. INTERNATIONAL JOURNAL OF NUMBER THEORY, 2019, 15 (06) : 1305 - 1321
[33] On Ramachandra's method for the mean value problems of various L-functions
Kamiya, Y
[J]. NUMBER THEORY AND ITS APPLICATIONS, 1999, 2 : 183 - 192
[34] An efficient algorithm for computing Dirichlet L-functions
Slezeviciene, R
[J]. INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2004, 15 (06) : 513 - 522
[35] Zeros of Dirichlet L-functions on the critical line
Sono, Keiju
[J]. JOURNAL OF NUMBER THEORY, 2025, 271 : 348 - 388
[36] The first moment of quadratic Dirichlet L-functions
Young, Matthew P.
[J]. ACTA ARITHMETICA, 2009, 138 (01) : 73 - 99
[37] Some Notes on Identities for Dirichlet L-functions
Ma, Rong
Zhang, Yu Long
Gruetzmann, Melchior
[J]. ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2014, 30 (05) : 747 - 754
[38] Mollification of the fourth moment of Dirichlet L-functions
Zacharias, Raphael
[J]. ACTA ARITHMETICA, 2019, 191 (03) : 201 - 257
[39] EULER PRODUCT ASYMPTOTICS FOR DIRICHLET L-FUNCTIONS
Kaneko, Ikuya
[J]. BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2022, 106 (01) : 48 - 56
[40] The third moment of quadratic Dirichlet L-functions
Young, Matthew P.
[J]. SELECTA MATHEMATICA-NEW SERIES, 2013, 19 (02): : 509 - 543

← 1 2 3 4 5 →