First moment of quadratic Hecke L-functions with lower order term

Peng Gao; Liangyi Zhao

doi:10.1016/j.jnt.2026.04.008

First moment of quadratic Hecke L-functions with lower order term

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 the first moment of the family of primitive quadratic Hecke L -functions in the Gaussian field using the method of double Dirichlet series under the Riemann hypothesis and the Lindelöf hypothesis. We obtain asymptotic formulas with secondary main terms and error terms of size that is one quarter of that of the main term.

源语言	英语
页（从-至）	160-185
页数	26
期刊	Journal of Number Theory
卷	289
DOI	https://doi.org/10.1016/j.jnt.2026.04.008
出版状态	已出版 - 12月 2026

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10.1016/j.jnt.2026.04.008

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@article{e3149138c5094965aa6fe021e1e1be12,

title = "First moment of quadratic Hecke L-functions with lower order term",

abstract = "We evaluate the first moment of the family of primitive quadratic Hecke L -functions in the Gaussian field using the method of double Dirichlet series under the Riemann hypothesis and the Lindel{\"o}f hypothesis. We obtain asymptotic formulas with secondary main terms and error terms of size that is one quarter of that of the main term.",

keywords = "Double Dirichlet series, First moment, Gaussian fields, Quadratic Hecke L-functions",

author = "Peng Gao and Liangyi Zhao",

note = "Publisher Copyright: {\textcopyright} 2026 The Author(s).",

year = "2026",

month = dec,

doi = "10.1016/j.jnt.2026.04.008",

language = "英语",

volume = "289",

pages = "160--185",

journal = "Journal of Number Theory",

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TY - JOUR

T1 - First moment of quadratic Hecke L-functions with lower order term

AU - Gao, Peng

AU - Zhao, Liangyi

PY - 2026/12

Y1 - 2026/12

N2 - We evaluate the first moment of the family of primitive quadratic Hecke L -functions in the Gaussian field using the method of double Dirichlet series under the Riemann hypothesis and the Lindelöf hypothesis. We obtain asymptotic formulas with secondary main terms and error terms of size that is one quarter of that of the main term.

AB - We evaluate the first moment of the family of primitive quadratic Hecke L -functions in the Gaussian field using the method of double Dirichlet series under the Riemann hypothesis and the Lindelöf hypothesis. We obtain asymptotic formulas with secondary main terms and error terms of size that is one quarter of that of the main term.

KW - Double Dirichlet series

KW - First moment

KW - Gaussian fields

KW - Quadratic Hecke L-functions

UR - https://www.scopus.com/pages/publications/105042459765

U2 - 10.1016/j.jnt.2026.04.008

DO - 10.1016/j.jnt.2026.04.008

M3 - 文章

AN - SCOPUS:105042459765

SN - 0022-314X

VL - 289

SP - 160

EP - 185

JO - Journal of Number Theory

JF - Journal of Number Theory

ER -

First moment of quadratic Hecke L-functions with lower order term

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