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^*

^*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 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.

Original language	English
Pages (from-to)	160-185
Number of pages	26
Journal	Journal of Number Theory
Volume	289
DOIs	https://doi.org/10.1016/j.jnt.2026.04.008
State	Published - Dec 2026

Keywords

Double Dirichlet series
First moment
Gaussian fields
Quadratic Hecke L-functions

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10.1016/j.jnt.2026.04.008

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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",

issn = "0022-314X",

publisher = "Academic Press Inc.",

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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

Abstract

Keywords

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