A note on the hybrid power mean involving the cubic Gauss sums and Kloosterman sums

Xiaoxue Li; Wenpeng Zhang; Xiaoxue Li; Wenpeng Zhang

doi:10.3934/math.2022881

AIMS Mathematics

2022, Volume 7, Issue 9: 16102-16111. doi: 10.3934/math.2022881

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Research article

A note on the hybrid power mean involving the cubic Gauss sums and Kloosterman sums

Xiaoxue Li ^{1
,
,},
Wenpeng Zhang ²

1.
School of Science, Xi'an Aeronautical Institute, Xi'an, Shaanxi, China
2.
School of Mathematics, Northwest University, Xi'an, Shaanxi, China

Received: 17 March 2022 Revised: 19 June 2022 Accepted: 22 June 2022 Published: 01 July 2022
MSC : 11L03, 11L05

The main purpose of this paper is to study the calculating problem of one kind hybrid power mean involving the cubic Gauss sums and Kloosterman sums, and using the elementary methods, analytic methods and the properties of the classical Gauss sums to give some interesting calculating formula for them. At the same time, the paper also provides an effective calculating method for the study of the hybrid power mean involving the $ k $-th Gauss sums and Kloosterman sums.
- the cubic Gauss sums,
- Kloosterman sums,
- hybrid power mean,
- elementary method,
- recurrence formula
Citation: Xiaoxue Li, Wenpeng Zhang. A note on the hybrid power mean involving the cubic Gauss sums and Kloosterman sums[J]. AIMS Mathematics, 2022, 7(9): 16102-16111. doi: 10.3934/math.2022881

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Abstract

The main purpose of this paper is to study the calculating problem of one kind hybrid power mean involving the cubic Gauss sums and Kloosterman sums, and using the elementary methods, analytic methods and the properties of the classical Gauss sums to give some interesting calculating formula for them. At the same time, the paper also provides an effective calculating method for the study of the hybrid power mean involving the $ k $-th Gauss sums and Kloosterman sums.

References

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