On the classical Gauss sums and their some new identities

Abstract

In this paper, we use the analytic methods and the properties of the classical Gauss sums to study the calculating problems of some Gauss sums involving the character of order 12 modulo an odd prime p, and obtain several new and interesting identities for them.

Keywords

• the character of order 12
• the classical gauss sums
• analytic methods
• identity
• calculating formula