Some new hybrid power mean formulae of trigonometric sums

Author:

Chen Li,Chen Zhuoyu

Abstract

AbstractWe 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.

Funder

National Natural Science Foundation of China

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Algebra and Number Theory,Analysis

Reference14 articles.

1. Chen, L., Hu, J.Y.: A linear recurrence formula involving cubic Gauss sums and Kloosterman sums. Acta Math. Sinica (Chin. Ser.) 61, 67–72 (2018)

2. Li, X.X., Hu, J.Y.: The hybrid power mean quartic Gauss sums and Kloosterman sums. Open Math. 15, 151–156 (2017)

3. Zhang, H., Zhang, W.P.: The fourth power mean of two-term exponential sums and its application. Math. Rep. 19, 75–83 (2017)

4. Zhang, W.P., Hu, J.Y.: The number of solutions of the diagonal cubic congruence equation mod p. Math. Rep. 20, 73–80 (2018)

5. Chen, Z.Y., Zhang, W.P.: On the fourth-order linear recurrence formula related to classical Gauss sums. Open Math. 15, 1251–1255 (2017)

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