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

[41] The third moment of quadratic Dirichlet L-functions [J].

Young, Matthew P. .

SELECTA MATHEMATICA-NEW SERIES, 2013, 19 (02) :509-543

[42] Some Notes on Identities for Dirichlet L-functions [J].

Rong MA ;

Yu Long ZHANG ;

Melchior GRTZMANN .

ActaMathematicaSinica(EnglishSeries), 2014, 30 (05) :747-754

[43] The fourth moment of quadratic Dirichlet L-functions [J].

Shen, Quanli .

MATHEMATISCHE ZEITSCHRIFT, 2021, 298 (1-2) :713-745

[44] Explicit estimates for the zeros of Hecke L-functions [J].

Zaman, Asif .

JOURNAL OF NUMBER THEORY, 2016, 162 :312-375

[45] The angle of large values of L-functions [J].

Hough, Bob .

JOURNAL OF NUMBER THEORY, 2016, 167 :353-393

[46] Correlation of shifted values of L-functions in the hyperelliptic ensemble [J].

Darbar, Pranendu ;

Maiti, Copal .

FINITE FIELDS AND THEIR APPLICATIONS, 2021, 76

[47] On the 2m-th power mean of Dirichlet L-functions with the weight of trigonometric sums [J].

Ma, Rong ;

Zhang, Junhuai ;

Zhang, Yulong .

PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 2009, 119 (04) :411-421

[48] First moment of central values of some primitive Dirichlet L-functions with fixed order characters [J].

Gao, Peng ;

Zhao, Liangyi .

JOURNAL OF NUMBER THEORY, 2024, 261 :125-142

[49] LARGE VALUES OF QUADRATIC DIRICHLET L-FUNCTIONS OVER MONIC IRREDUCIBLE POLYNOMIAL IN Fq[t] [J].

Darbar, Pranendu ;

Maiti, Gopal .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2024, 152 (08) :3243-3254

[50] Conditional estimates for the logarithmic derivative of Dirichlet L-functions [J].

Chirre, Andres ;

Hagen, Markus Valas ;

Simonic, Aleksander .

INDAGATIONES MATHEMATICAE-NEW SERIES, 2024, 35 (01) :14-27

← 1 2 3 4 5 →