L-函数的均值估计以及数论中一些重要和式的均值研究，一直以来都是解析数论中的重要研究课题，许多问题都与它们密切相关。近年来，关于L-函数的均值研究取得了新的进展，其中关于L-函数在s=1/2处四次均值问题，M.Young已经给出了很好的结果。本项目旨在研究L-函数各种不同形式的均值估计，并以此为基础研究L-函数在指数和、特征和、Kloosterman和等和式算术性质研究中的应用。计划通过本项目的实施，给出L-函数的各种混合均值的上界估计或渐近性质，并通过寻求L-函数与以上和式之间的关系，更好的研究这些和式的算术性质。

The estimation for L-functions and the mean value of some famous summations are all the important problem in analytic number theory. They have close relations with many number theory problems and very important applications. Recently, there has been some important progress on this direction, specifically for the fourth mean value in s=1/2 of Dirichlet L-functions, M.Young has made remarkable progress. In this project, we aim to work on the upper or lower bound estimates or distribution properties of mean value of some L-functions, and to study the application of these mean values of L-functions in exponential sums，character sums, Kloosterman sums and some generalized sums. Through this project, we plan to give some upper bound estimates or asymptotic properties of mean value of L-functions, and want to explore the relationship of L-functions and some famous summations to get a few arithmetic properties of these summations.