Some new hybrid power mean formulae of trigonometric sums

Abstract

Abstract We apply the analytic method and the properties of the classical Gauss sums to study the computational problem of a certain hybrid power mean of the trigonometric sums and to prove several new mean value formulae for them. At the same time, we also obtain a new recurrence formula involving the Gauss sums and two-term exponential sums.

Keywords

• Cubic Gauss sums
• Two-term exponential sums
• Hybrid power mean
• Computational formula