自守L-函数理论是Langlands纲领的核心内容，也是数论、代数、调和分析等学科交汇点上的热点领域，这个领域既包含着解决数学问题的重大潜力，也包含着许多迷人的猜想。这些猜想不仅是一颗颗璀璨的宝石，而且是一只只“能生金蛋的母鸡”，推动数学的发展。 本项目的研究围绕着三个猜想展开：一、研究GL(3)上自守L-函数在临界直线上的平方积分均值估计，给出Lindelof猜想成立的条件。二、研究Hecke 特征值乘积在算术级数中的符号变化情况，得到非正项和非负项个数的下界，为Ramanujan猜想提供理论依据。三、研究Möbius函数与Hecke 特征值及加性特征在特殊序列中的振荡规律，对Sarnak猜想作进一步诠释。本项目旨在应用经典解析数论中的各种方法和技巧，研究自守L-函数及其傅里叶系数的解析性质，进而将自守形式理论的相关结果应用到经典解析数论的问题中，找到经典解析数论与自守形式理论的结合点。

Automorphic L-function is the core of Langlands Program and the intersection of number theory, algebra and harmonic analysis. In this area, there are great potentials to solve mathematical problems and many charming conjectures, which are not only the bright diamonds, but also the "hen that can lay golden eggs". The research include: 1) we will study the integral mean value of automorphic L-functions in the critical line to get the condition for Lindelof Hypothesis. 2) we will study the sign changes of the product of Hecke eigenvalue, which can provide the theoretical proof for Ramanujan Conjecture. 3) we will study the oscilation between Möbius function, Hecke eigenvalue and additive character in special sequence, which is the further explanation for Sarnak Conjecture. The aim of this program is applying the methods of analytic number theory to automorphic forms and solving the problems in number theory through automorphic forms, in order to find the optimum combining site between the classical analytic number theory and automorphic forms.