On a hybrid mean value of the character sums over short intervals

Mean Value of Hardy Sums over Short Intervals

The main purpose of this paper is to study the mean value properties of certain Hardy sums over short intervals by using the mean value theorems of the Dirichlet L-functions, and to give two interesting asymptotic formulae.

A hybrid mean value involving a new Gauss sums and Dedekind sums

‎In this paper‎, ‎we introduce a new sum‎ ‎analogous to Gauss sum‎, ‎then we use the properties of the‎ ‎classical Gauss sums and analytic method to study the hybrid mean‎ ‎value problem involving this new sums and Dedekind sums‎, ‎and‎ ‎give an interesting identity for it.

Double Character Sums over Subgroups and Intervals

We estimate double sums Sχ(a, I,G) = ∑

On the Hybrid Mean Value of Cochrane Sums and Two-term Exponential Sums

A Hybrid Mean Value Involving Dedekind Sums and the General Exponential Sums

The main purpose of this paper is using the analytic method, A. Weil's classical work for the upper bound estimate of the general exponential sums, and the properties of Gauss sums to study the hybrid mean value problem involving Dedekind sums and the general exponential sums and give a sharp asymptotic formula for it.