Gauss sums for U(2n, q2)

On Gauss-Jacobi sums

In this paper, we introduce a kind of character sum which simultaneously generalizes the classical Gauss and Jacobi sums, and show that this “Gauss-Jacobi sum” also specializes to the Kloosterman sum in a particular case. Using the connection to the Kloosterman sums, we obtain in some special cases the upper bound (the “Weil bound”) of the absolute values of the Gauss-Jacobi sums. We also discu...

Half Gauss Sums

Exponential Sums, Gauss Sums and Cyclic Codes

The dissertation consists of three articles in which the evaluation of certain exponential sums and Gauss sums and bounds for the absolute values of exponential sums are considered. The summary part of the thesis provides interpretations in terms of coding theory for the results obtained in the articles.

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.

Kummer’s Conjecture for Cubic Gauss Sums

for primes p ≡ 1 (mod 3) up to 500, and found that Sp/(2√p) lay in the intervals [−1,− 12 ], (− 12 , 12 ), [ 1 2 , 1] with frequencies approximately in the ratio 1 : 2 : 3. He conjectured, somewhat hesitantly, that this might be true asymptotically. Kummer’s conjecture was disproved by Heath-Brown and Patterson [4]. In order to state their result we must introduce a little notation. Let ω = exp...