关于自守L-函数的系数的研究综述  

A Survey on Coefficients of Automorphic L-functions

作　　者：蒋玉蛟 吕广世[2] JIANG Yujiao;Lu Guangshi(School of Mathematics and Statistics,Shandong University(Weihai),Weihai,Shandong,264209,P.R.China;School of Mathematics,Shandong University,Jinan,Shandong,250100,P.R.China)

机构地区：[1]山东大学(威海)数学与统计学院,威海山东264209 [2]山东大学数学学院,济南山东250100

出　　处：《数学进展》2023年第2期201-223,共23页Advances in Mathematics（China）

基　　金：Jiang is supported by NSFC(No.12271297);Young Scholars Program of Shandong University at Weihai(No.20820211012);Lü is supported in part by NSFC(No.12031008),Ministry of Education of China(No.IRT16R43);Taishan Scholars Project and the National Key Research and Development Program of China(No.2021YFA1000700)。

摘　　要：本文试图总结近年来关于自守L-函数系数估计的一些研究进展.我们主要讨论了四个方面的问题:高阶群上Fourier系数的指数和、Fourier系数的高次均值、高阶群上的Bombieri-Vinogradov定理和高阶群上的平移卷积和。In this paper we try to summarize some recent progress on the estimation of coefficients of L-functions in some concrete aspects.We mainly talk about four problems:exponential sums with Fourier coeficients on higher rank groups,higher power moments of Fourier coefficients,the Bombieri-Vinogradov theorem on higher rank groups,and the shifted convolution sums on higher rank groups.

关 键 词：FOURIER系数 自守L-函数 

分 类 号：O156[理学—数学]