Dirichlet L-函数的均值

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

数学季刊 ›› 2025, Vol. 40 ›› Issue (4): 360-371.doi: 10.13371/j.cnki.chin.q.j.m.2025.04.003

Dirichlet L-函数的均值

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

收稿日期:2025-08-26 出版日期:2025-12-30 发布日期:2025-12-30
作者简介: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.
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).

Moments of Dirichlet L-Functions

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

Received:2025-08-26 Online:2025-12-30 Published:2025-12-30
About author: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.
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).

摘要/Abstract

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

Abstract: 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.

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

中图分类号:

O156

黄炳荣, 黄俊皓. Dirichlet L-函数的均值[J]. 数学季刊, 2025, 40(4): 360-371.

HUANG Bing-rong, HUANG Jun-hao. Moments of Dirichlet L-Functions[J]. Chinese Quarterly Journal of Mathematics, 2025, 40(4): 360-371.

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Dirichlet L-函数的均值

Moments of Dirichlet L-Functions

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