A hybrid mean value involving two-term exponential sums and polynomial character sums

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.

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.

On the General Dedekind Sums and Two-Term Exponential Sums

We use the analytic methods and the properties of Gauss sums to study the computational problem of one kind hybrid mean value involving the general Dedekind sums and the two-term exponential sums, and give an interesting computational formula for it.

Sparse Polynomial Exponential Sums

(1.2) f(x) = a1x k1 + · · ·+ arx with 0 < k1 < k2 < · · · < kr. We assume always that the content of f , (a1, a2, . . . , ar), is relatively prime to the modulus q. Let d = d(f) = kr denote the degree of f and for any prime p let dp(f) denote the degree of f read modulo p. A fundamental problem is to determine whether there exists an absolute constant C such that for an arbitrary positive integ...