A new reciprocity formula of Dedekind sums and its applications

Abstract

Our main purpose of this article was using the analytic methods and the properties of Dirichlet $ L $-functions to study the properties of Dedekind sums and give a new reciprocity formula for it. As its applications, some exact calculating formula for one kind mean square value of Dirichlet $ L $-fuctions with the weight of the character sums were obtained.

Keywords

• dedekind sums
• reciprocity formula
• dirichlet $ l $-functions
• the mean square value of $ l $-function