算术数列中Fourier系数的均值估计  

Estimation of Mean Value of Fourier Coefficients in Arithmetic Series

作　　者：武毅 WU Yi(School of Mathematics and Statistics,North China University of Water Resources and Electric Power,Zhengzhou 450046,China)

机构地区：[1]华北水利水电大学数学与统计学院,河南郑州450046

出　　处：《兰州文理学院学报(自然科学版)》2025年第1期1-6,共6页Journal of Lanzhou University of Arts and Science(Natural Sciences)

摘　　要：设f(z)是全模群上权为偶数k的全纯本原尖形式,L(s,sym^(4)f)是与f对应的4次对称幂L-函数,λ_(sym^(4)f)(n)是L(s,sym^(4)f)的Fourier展开的第n个标准化系数.本文借助对称幂L-函数的解析性质研究了算术数列中4次对称幂L-函数Fourier系数的均值估计,即Σ_(n≤x,n≡l(q))λ_(sym^(4)f)(n^(2)).Let f(z)be a holomorphic primitive cusp form of even integral weightkfor the full modular group.Denote by λ_(sym^(4)f)(n)the nth normalized coefficient of the Fourier expansion of the 4th symmetric power L-function associated to f.By using the properties of symmetric power L-functions,the average behavior of the Fourier coefficients of the 4th symmetric power L-function over arithmetic progressions is studied in this paper,i.e Σ_(n≤x,n≡l(q))λ_(sym^(4)f)(n^(2)).

关 键 词：全纯本原尖形式 对称幂L-函数 算术数列 FOURIER系数 

分 类 号：O156.4[理学—数学]