On The Weighted Mean Of The Generalized Dedekind And Of Dirichlet L-function Of The Reciprocal Of A Weighted Mean

Dirichlet L-functions, Gauss s.ums and Dedekind sums play prominent roles in the study of the analytic number theory and modular forms theory. So it is very important to find some relationships between them. In this thesis, we mainly study two kind of hybrid mean values as following:On the mean value of a generalized Dedekind sums with the weight of Hurwitz zeta-functions. The main purpose of the first chapter is using the theorem for Dirichlet L-functions and the estimates for charater sums to study the distribution property of the m-th power mean Sm(a,n,q). A sharper asymptotic formula is derived.A hybrid mean value of the inversion of L-functions and Gauss sums. The main purpose of the second chapter is using the estimates for character sums and the analytic method to study the asymptoticdistribution of the first power mean ,and give a ac-curalate asymptotic formula.