The hybrid power mean of the generalized Gauss sums

Abstract

Abstract The main purpose of this paper is using the analytic method and the orthogonal properties of the character sums to study the computational problem of one kind hybrid power mean of the generalized Gauss sums mod p $\operatorname{mod}\ p$ , an odd prime with p ≡ 1 mod 3 $p\equiv 1\operatorname{mod}\ 3$ , and give some exact computational formulas for this kind hybrid power mean.

Keywords

• generalized Gauss sums
• hybrid power mean
• analytic method
• computational formula