ON MIXED TWO-TERM EXPONENTIAL SUMS

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.

Pure and Mixed Exponential Sums

We obtain explicit formulae and sharp estimates for pure and mixed exponential sums of the type S(f, pm) = ∑pm x=1 epm (f(x)) and S(χ, f, pm) = ∑pm x=1 χ(x)epm (f(x)), where p m is a prime power with m ≥ 2, χ is a multiplicative character (mod pm), and f is a polynomial. For nonconstant f (mod p) we prove |S(χ, f, pm)| ≤ 2d 1 M+1 p m(1− 1 M+1 ) where d is the degree of f and M is the maximum mu...

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

Exponential Sums on A

Let d = degree of f and write f = f (d) + f (d−1) + · · ·+ f , where f (j) is homogeneous of degree j. A by now classical theorem of Deligne[2, Théorème 8.4] says that if (p, d) = 1 and f (d) = 0 defines a smooth hypersurface in P, then L(A, f ; t) n+1 is a polynomial of degree (d − 1), all of whose reciprocal roots have absolute value equal to q. This implies the estimate |S(A(Fqi), f)| ≤ (d− ...

On Exponential Sums