Twisted first moment of central values of primitive quadratic Dirichlet L-functions

Peng Gao; Liangyi Zhao

doi:10.4064/aa240617-6-11

Twisted first moment of central values of primitive quadratic Dirichlet L-functions

Peng Gao
, Liangyi Zhao

School of Mathematical Sciences

University of New South Wales

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

Abstract

We evaluate the twisted first moment of central values of the family of primitive quadratic Dirichlet L-functions using the method of double Dirichlet series together with a recursive argument. Our main result is an asymptotic formula with an error term of size that is the square root of that of the main term.

Original language	English
Pages (from-to)	101-122
Number of pages	22
Journal	Acta Arithmetica
Volume	219
Issue number	2
DOIs	https://doi.org/10.4064/aa240617-6-11
State	Published - 2025

Keywords

double Dirichlet series
first moment
quadratic Dirichlet L-functions

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title = "Twisted first moment of central values of primitive quadratic Dirichlet L-functions",

abstract = "We evaluate the twisted first moment of central values of the family of primitive quadratic Dirichlet L-functions using the method of double Dirichlet series together with a recursive argument. Our main result is an asymptotic formula with an error term of size that is the square root of that of the main term.",

keywords = "double Dirichlet series, first moment, quadratic Dirichlet L-functions",

author = "Peng Gao and Liangyi Zhao",

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AU - Gao, Peng

AU - Zhao, Liangyi

N1 - Publisher Copyright: © Instytut Matematyczny PAN, 2025.

PY - 2025

Y1 - 2025

N2 - We evaluate the twisted first moment of central values of the family of primitive quadratic Dirichlet L-functions using the method of double Dirichlet series together with a recursive argument. Our main result is an asymptotic formula with an error term of size that is the square root of that of the main term.

AB - We evaluate the twisted first moment of central values of the family of primitive quadratic Dirichlet L-functions using the method of double Dirichlet series together with a recursive argument. Our main result is an asymptotic formula with an error term of size that is the square root of that of the main term.

KW - double Dirichlet series

KW - first moment

KW - quadratic Dirichlet L-functions

UR - https://www.scopus.com/pages/publications/105012861818

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DO - 10.4064/aa240617-6-11

M3 - 文章

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VL - 219

SP - 101

EP - 122

JO - Acta Arithmetica

JF - Acta Arithmetica

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ER -

Twisted first moment of central values of primitive quadratic Dirichlet L-functions

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