The Mean Values of Character Sums and Their Applications

Abstract

In this paper, we use the elementary methods and properties of classical Gauss sums to study the calculation problems of some mean values of character sums of special polynomials, and obtained several interesting calculation formulae for them. As an application, we give a criterion for determining that 2 is the cubic residue for any odd prime p.

Keywords

• character sums of polynomials
• mean value
• classical Gauss sums
• analytic methods
• calculation formula