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

Peng Gao; Liangyi Zhao

doi:10.1016/j.jnt.2024.02.007

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

Peng Gao
, Liangyi Zhao^*

^*此作品的通讯作者

数学科学学院

University of New South Wales

科研成果: 期刊稿件 › 文章 › 同行评审

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.

源语言	英语
页（从-至）	125-142
页数	18
期刊	Journal of Number Theory
卷	261
DOI	https://doi.org/10.1016/j.jnt.2024.02.007
出版状态	已出版 - 8月 2024

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10.1016/j.jnt.2024.02.007

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@article{85770f0d020c40c0b7642f5addb3adad,

title = "First moment of central values of some primitive Dirichlet L-functions with fixed order characters",

abstract = "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.",

keywords = "Central values, Dirichlet L-functions, Gauss sums, Moments of L-functions",

author = "Peng Gao and Liangyi Zhao",

note = "Publisher Copyright: {\textcopyright} 2024 The Author(s)",

year = "2024",

month = aug,

doi = "10.1016/j.jnt.2024.02.007",

language = "英语",

volume = "261",

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T1 - First moment of central values of some primitive Dirichlet L-functions with fixed order characters

AU - Gao, Peng

AU - Zhao, Liangyi

PY - 2024/8

Y1 - 2024/8

N2 - 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.

AB - 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.

KW - Central values

KW - Dirichlet L-functions

KW - Gauss sums

KW - Moments of L-functions

UR - https://www.scopus.com/pages/publications/85189011639

U2 - 10.1016/j.jnt.2024.02.007

DO - 10.1016/j.jnt.2024.02.007

M3 - 文章

AN - SCOPUS:85189011639

SN - 0022-314X

VL - 261

SP - 125

EP - 142

JO - Journal of Number Theory

JF - Journal of Number Theory

ER -

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

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