On the sixth power mean values of a generalized two-term exponential sums

Abstract

This paper examines the evaluations of sixth power mean values of a generalized two-term exponential sums. In the case $ p\equiv 3\bmod 4 $, we try to establish two precise formulas by applying the properties of character sums and the number of the solutions of relevant congruence equations modulo an odd prime $ p $.

Keywords

• the two-term exponential sums
• sixth power mean values
• elementary method
• congruence equation
• calculating formula