Two Kinds Hybrid Power Mean Involving Two-Term Exponential Sums and Dedekind Sums

TL;DR

This paper introduces new asymptotic formulas for hybrid power means involving exponential and Dedekind sums, using analytic methods and quadratic residual transformations, thereby generalizing previous results.

Contribution

It provides a novel generalization of existing formulas for hybrid power means involving exponential and Dedekind sums using advanced analytic techniques.

Findings

Derived two asymptotic formulas for hybrid power means

Generalized previous results in the field

Applied quadratic residual transformation techniques

Abstract

The main purpose of this article is using the analytic mathods and the quadratic residual transformation technique, and properties of Dedekind sums to study the calculating problem of two kinds hybrid power mean involving the two-term exponential sums and Dedekind sums, and give two asymptotic formulas for it. This work is a generalization for existing conclusions.