摘要
自守形式理论是现代数论的重要课题.自守形式的傅里叶系数蕴含了深刻的数论性质,其在数论中有许多应用.设f是本原Maass尖形式,λ_(f)(n)是它在尖点无穷远处的第n个傅里叶系数.结合经典的解析方法和一些本原自守L-函数的性质,本文研究了全模群上Maass尖形式的傅里叶系数在算术级数上的分布性质,得到了相应的渐近公式.
Automorphic forms are important topics in modern number theory.Fourier coefficients of automorphic forms imply profound properties,which have many applications.Let f be a primitive Maass cusp form andλ_(f)(n)be its nth Fourier coefficient at the cusp infinity.Applying classical analytic methods and properties of primitive automorphic L-functions,this paper investigates the distribution of Fourier coefficients of Maass cusp forms over arithmetic progressions for the full modular group,and establishes the corresponding asymptotic formula.
作者
潘慧敏
魏琳丽
劳会学
PAN Huimin;WEI Linli;LAO Huixue(School of Mathematics and Statistics,Shandong Normal University,Jinan 250014,China)
出处
《纯粹数学与应用数学》
2024年第1期168-180,共13页
Pure and Applied Mathematics
基金
山东省自然科学基金(ZR2018MA003)。
