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^*

^*Corresponding author for this work

School of Mathematical Sciences

University of New South Wales

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	125-142
Number of pages	18
Journal	Journal of Number Theory
Volume	261
DOIs	https://doi.org/10.1016/j.jnt.2024.02.007
State	Published - Aug 2024

Keywords

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

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10.1016/j.jnt.2024.02.007

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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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journal = "Journal of Number Theory",

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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

Abstract

Keywords

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