The generalized quadratic Gauss sums and its sixth power mean

Xingxing Lv; Wenpeng Zhang; Xingxing Lv; Wenpeng Zhang

doi:10.3934/math.2021654

AIMS Mathematics

2021, Volume 6, Issue 10: 11275-11285. doi: 10.3934/math.2021654

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Research article Special Issues

The generalized quadratic Gauss sums and its sixth power mean

Xingxing Lv ,
Wenpeng Zhang ^,

School of Mathematics, Northwest University, Xi'an, Shaanxi, China

Received: 06 May 2021 Accepted: 28 July 2021 Published: 04 August 2021
MSC : 11L03, 11L07

In this article, we using elementary methods, the number of the solutions of some congruence equations and the properties of the Legendre's symbol to study the computational problem of the sixth power mean of a certain generalized quadratic Gauss sums, and to give an exact calculating formula for it.
- congruence equation,
- a certain generalized quadratic Gauss sums,
- the sixth power mean,
- calculating formula
Citation: Xingxing Lv, Wenpeng Zhang. The generalized quadratic Gauss sums and its sixth power mean[J]. AIMS Mathematics, 2021, 6(10): 11275-11285. doi: 10.3934/math.2021654

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Abstract

In this article, we using elementary methods, the number of the solutions of some congruence equations and the properties of the Legendre's symbol to study the computational problem of the sixth power mean of a certain generalized quadratic Gauss sums, and to give an exact calculating formula for it.

References

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