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不同序列上傅里叶系数的一致均值估计

Uniform Mean Estimates ofFourier Coefficients over Different Sequences
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摘要 在解析数论领域,探讨全纯尖形式的傅里叶系数具有重要的理论价值.通过复变函数的积分技巧,结合自守L-函数的凸界以及积分均值估计方法,研究了不同序列上傅里叶系数的一致均值估计,形式化表达为∑n≤xλf nλf n j,j=2,3,其中f是全模群Γ=SL(2,Z)上权为偶数k的Hecke特征型,λf n是其在尖点∞处傅里叶展开的第n个标准化傅里叶系数. In the field of analytic number theory,exploring the Fourier coefficients of holomorphic modular form holds significant theoretical value.This paper will use the method of integration of complex variable functions,combing with the convexity bounds of the automorphic L-function and estimates of the mean value,studies the uniform mean estimates of Fourier coefficients on different sequences.The formal expression is as follows∑n≤xλf nλf n j,j=2,3,where f be a Hecke eigenform of even integral weights k for the full modular groupΓ=SL(2,Z)andλf n be the nth normalized Fourier coefficient of its Fourier expansion at the cusp∞.
作者 李丽娟 LI Li-juan(College of Mathematics and Statistics,North China University ofWater Resources and Electric Power,Zhengzhou 450046,China)
机构地区 华北水利水电大学数学与统计学院
出处 《兰州文理学院学报(自然科学版)》 2025年第2期34-39,共6页 Journal of Lanzhou University of Arts and Science(Natural Sciences)
关键词 全纯尖形式 傅里叶系数 自守L-函数 一致均值估计 cusp form Fourier coefficient automorphic L-function uniform mean estimate
分类号 O156.4 [理学—基础数学]
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兰州文理学院学报(自然科学版)
2025年 第2期

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