算术数列中Fourier系数的均值估计
Estimation of Mean Value of Fourier Coefficients in Arithmetic Series
武毅1
作者信息
- 1. 华北水利水电大学数学与统计学院,河南郑州 450046
- 折叠
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,sym4 f)是与f对应的4次对称幂L-函数,λsym4 f(n)是L(s,sym4 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 ∑n≤xn≡l(q)λsym4 f(n2).
Abstract
Letf(z)be a holomorphic primitive cusp form of even integral weightk for the full modular group.Denote by λsym4 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 pow-er L-function over arithmetic progressions is studied in this paper,i.e.∑n≤xn≡l(q) λsym4 f(n2).
关键词
全纯本原尖形式/对称幂L-函数/算术数列/Fourier系数Key words
holomorphic primitive cusp form/symmetric power L-function/arithmetic pro-gressions/Fourier coefficient引用本文复制引用
出版年
2025
NETL
NSTL
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