The fourth power mean of the generalized quadratic Gauss sums associated with some Dirichlet characters

Abstract

In this paper, the fourth power mean values of the generalized quadratic Gauss sums associated with the $ 3 $-order and $ 4 $-order Dirichlet characters are given by using the properties of the Dirichlet characters and Gauss sums.

Keywords

• generalized quadratic gauss sums
• the fourth power mean
• $ k $-order dirichlet character
• calculating formula