两平方和整数列上尖形式傅里叶系数的高阶矩  

On Higher Moments of Cusp Form Fourier Coefficients over Sum of Two Squares

作　　者：华国栋 HUA Guodong(School of Mathematics and Statistics,Weinan Normal University,Weinan,Shaanci,714099,P.R.China)

机构地区：[1]渭南师范学院数学与统计学院,陕西渭南714099

出　　处：《数学进展》2024年第1期115-124,共10页Advances in Mathematics（China）

基　　金：Supported in part by the National Key Research and Development Program of China(No.2021YFA1000700);Natural Science Basic Research Program of Shaanxi(Nos.2023-JC-QN-0024,2023-JC-YB-077);Foundation of Shaanxi Educational Committee(No.2023-JC-YB-013);Shaanxi Fundamental Science Research Project for Mathematics and Physics(No.22JSQ010)。

摘　　要：取f,g与h为在全模群Γ=SL(2,Z)上偶数权分别为k_(1),k_(2)与k_(3)的三个不同的本原全纯模形式.记λ_(f)(n),λ_(g)(n)与λ_(h)(n)分别为f,g与h的n阶正规化傅里叶系数.本文考察两平方和整数列上涉及算术函数λ_(f)(n),λ_(g)(n)与λ_(h)(n)的求和抵消问题,对任意ε>0,建立了如下的结论:■其中1≤i≤2和j≥1为任意固定的正整数.Let f,g and h be three distinct primitive holomorphic cusp forms of even integral weights k_(1),k_(2) and k_(3) for the full modular group F=SL(2,Z),respectively.And letλ_(f)(n),λ_(g)(n)andλ_(h)(N)denote the nth normalized Fourier coefficients of f,g and h,respectively.In this paper,we consider the cancellations of sums related to arithmetic functionsλ_g(n),λ_h(n),λ_f(n)over sum of two squares and establish the following result,■for anyε>0,where 1≤i≤2,j≥1 are any fixed positive integers.

关 键 词：Hecke特征型 傅里叶系数 自守L-函数 

分 类 号：O156[理学—数学]