First moment of central values of some primitive Dirichlet L-functions with fixed order characters

被引：0

作者：

Gao, Peng ^{[1
]}

Zhao, Liangyi ^{[2
]}

机构：

[1] Beihang Univ, Sch Math Sci, Beijing 100191, Peoples R China

[2] Univ New South Wales, Sch Math & Stat, Sydney, NSW 2052, Australia

来源：

JOURNAL OF NUMBER THEORY | 2024年 / 261卷

关键词：

Central values; Dirichlet L-functions; Gauss sums; Moments of L-functions; SERIES;

D O I：

10.1016/j.jnt.2024.02.007

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We evaluate asymptotically the smoothed first moment of central values of families of primitive cubic, quartic and sextic Dirichlet L -functions, using the method of double Dirichlet series. Quantitative non -vanishing results for these L -values are also proved. (c) 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http:// creativecommons .org /licenses /by /4 .0/).

引用

页码：125 / 142

页数：18

共 19 条

[1] Mean values with cubic characters [J].

Baier, Stephan ;

Young, Matthew P. .

JOURNAL OF NUMBER THEORY, 2010, 130 (04) :879-903

[2] A theorem on analytic continuation of functions in several variables [J].

Bochner, S .

ANNALS OF MATHEMATICS, 1938, 39 :14-19

[3]

Brubaker B., 2003, Thesis (Ph.D.)-

[4]

Cech M, 2023, Arxiv, DOI arXiv:2110.04409

[5]

Davenport H., 2000, GRADUATE TEXTS MATH, V74

[6]

David Chantal, 2021, FORUM MATH SIGMA, V9, pe69

[7] Multiple Dirichlet series and moments of zeta and L-functions [J].

Diaconu, A ;

Goldfeld, D ;

Hoffstein, J .

COMPOSITIO MATHEMATICA, 2003, 139 (03) :297-360

[8] Moments of central values of quartic Dirichlet L-functions [J].

Gao, Peng ;

Zhao, Liangyi .

JOURNAL OF NUMBER THEORY, 2021, 228 :342-358

[9] Moments of quadratic Hecke L-functions of imaginary quadratic number fields [J].

Gao, Peng ;

Zhao, Liangyi .

JOURNAL OF NUMBER THEORY, 2020, 209 :359-377

[10] EISENSTEIN SERIES OF 1/2-INTEGRAL WEIGHT AND THE MEAN-VALUE OF REAL DIRICHLET L-SERIES [J].

GOLDFELD, D ;

HOFFSTEIN, J .

INVENTIONES MATHEMATICAE, 1985, 80 (02) :185-208

← 1 2 →