With The Generalized Dedekind And The Associated Mean Of The Mixture

The study on the value mean about all kinds of number theory’s functions in the analytic theory is always the important issue of many number theorists, including Dedekind sums, Kloosterman sums, generalized Dedekind sums, Gauss sums and character sums etc have the important significance and they each other have closely connection. Many important conclusions have been given, which make an important contribution to number theory’s farther development and inspire we make progress in the number theory’s research, we make farther study based on the interest on it and the predecessor’s research achievement. The main achievements that the hybrid mean value involving generalized Dedekind sums and Kloosterman sums contained dissertation are as follows: Above issues in this paper, We use the properties of Gauss sums, the arithmetical properties of generalized Dedekind sums, the mean value theorem of Dirichlet L-functions and the estimates for character sums to study the hybrid mean value problems involving generalized Dedekind sums and Kloosterman sums, and give some strong asymptotic formulas for it.