Some identities involving Gauss sums

Abstract

We calculate several identities involving some Gauss sums of the $ 2^k $-order character modulo an odd prime $ p $ by using the elementary and analytic methods, and finally give several exact and interesting formulae for them. The properties of the classical Gauss sums play an important role in the proof of this paper.

Keywords

• 2^k-order character
• the classical gauss sums
• analytic methods
• identity
• calculating formula