New Identities Dealing with Gauss Sums

Abstract

In this article, we used the elementary methods and the properties of the classical Gauss sums to study the problem of calculating some Gauss sums. In particular, we obtain some interesting calculating formulas for the Gauss sums corresponding to the eight-order and twelve-order characters modulo p, where p be an odd prime with p=8k+1 or p=12k+1.

On the Fourth Hybrid Power Mean Involving the Generalized Gauss Sums

“…Tere are a number of studies with regard to the Gauss sums and their recursion properties, which can be found in [6][7][8][9][10][11][12][13][14][15].…”

The Mean Values of Character Sums and Their Applications

“…Many number theory problems are closely related to it. Some works can be found in references [1][2][3][4][5][6][7][8][9][10][11][12][13], which will not be listed here. For example, if p is a prime with p = 4k + 1, then p can be expressed as the sum of two squares of positive integers.…”