On the Hybrid Mean Value of Generalized Dedekind Sums, Generalized Hardy Sums and Kloosterman Sums

TL;DR

This paper investigates the hybrid mean values of generalized Dedekind sums, Hardy sums, and Kloosterman sums, providing exact formulas using properties of Gauss sums and Dirichlet L-functions.

Contribution

It introduces new exact computational formulas for hybrid mean values involving these sums, expanding understanding of their interrelations.

Findings

Derived explicit formulas for hybrid mean values

Utilized properties of Gauss sums and Dirichlet L-functions

Enhanced computational methods for generalized sums

Abstract

The main purpose of this paper is to study the hybrid mean value problem involving generalized Dedekind sums, generalized Hardy sums and Kloosterman sums, and give some exact computational formulae for them by using the properties of Gauss sums and the mean value theorem of the Dirichlet L-function.