A hybrid mean value of Dedekind sums and Kloosterman sums

In this paper, we use the properties of Gauss sums and analytic methods to study the hybrid mean value problems involving Dedekind sums and Kloosterman sums, and give an interesting asymptotic formula for it. At the same time, we can also use the similar methods to deal with the other related sums, such as Cochrane sums.