A remark for Gauss sums of order 3 and some applications for cubic congruence equations

Abstract

In this paper, we give some relations between Gauss sums of order 3. As application, we give the number of solutions of some cubic diagonal equations. These generalize the earlier results obtained by Hong-Zhu and solve the sign problem raised by Zhang-Zhang.

Keywords

• gauss sum
• exponential sum
• diagonal cubic form
• congruence equations
• prime