Dirichlet L-函数的均值

黄炳荣, 黄俊皓

doi:10.13371/j.cnki.chin.q.j.m.2025.04.003

数学季刊 >

2025 , Vol. 40 >Issue 4: 360 - 371

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2025.04.003

Dirichlet L-函数的均值

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Data Science Institute and School of Mathematics, Shandong University, Jinan 250100, China

HUANG Bing-rong, professor of Shandong University, engages in analytic number theory; HUANG Jun-hao, master student of Shandong University, engages in analytic number theory.

收稿日期: 2025-08-26

网络出版日期: 2025-12-30

基金资助

Supported by the National Key R&D Program of China (Grant No. 2021YFA1000700) and National Natural Science Foundation of China (Grant No. 12031008).

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Moments of Dirichlet L-Functions

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Data Science Institute and School of Mathematics, Shandong University, Jinan 250100, China

HUANG Bing-rong, professor of Shandong University, engages in analytic number theory; HUANG Jun-hao, master student of Shandong University, engages in analytic number theory.

Received date: 2025-08-26

Online published: 2025-12-30

Supported by

Supported by the National Key R&D Program of China (Grant No. 2021YFA1000700) and National Natural Science Foundation of China (Grant No. 12031008).

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摘要

In this paper, we establish asymptotic formulas for a cubic moment of Dirichlet L-functions restricted to a coset, as well as for a mixed moment of Dirichlet L-functions and twists of GL(2) L-functions along a coset. Our main tool is a power-saving estimate of bilinear forms of hyper-Kloosterman sums due to Kowalski–Michel–Sawin.

关键词： Moment; Twist; Dirichlet L-functions; Coset

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黄炳荣, 黄俊皓 . Dirichlet L-函数的均值[J]. 数学季刊, 2025 , 40(4) : 360 -371 . DOI: 10.13371/j.cnki.chin.q.j.m.2025.04.003

Abstract

Key words： Moment; Twist; Dirichlet L-functions; Coset

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