A note on two-term exponential sum and the reciprocal of the quartic Gauss sums

Abstract

Abstract The main purpose of this article is by using the properties of the fourth character modulo a prime p and the analytic methods to study the calculating problem of a certain hybrid power mean involving the two-term exponential sums and the reciprocal of quartic Gauss sums, and to give some interesting calculating formulae of them.

Keywords

• Reciprocal of the quartic Gauss sums
• Two-term exponential sums
• Hybrid power means
• Analytic methods