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

Wenxu Ge; Weiping Li; Tianze Wang; Wenxu Ge; Weiping Li; Tianze Wang

doi:10.3934/math.2022595

AIMS Mathematics

2022, Volume 7, Issue 6: 10671-10680. doi: 10.3934/math.2022595

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

1.
School of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou 450046, China
2.
School of Mathematics and Information Sciences, Henan University of Economics and Law, Zhengzhou 450046, China

Received: 03 October 2021 Revised: 17 March 2022 Accepted: 21 March 2022 Published: 30 March 2022
MSC : 11T23, 11T24

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.
- Gauss sum,
- exponential sum,
- diagonal cubic form,
- congruence equations,
- prime
Citation: Wenxu Ge, Weiping Li, Tianze Wang. A remark for Gauss sums of order 3 and some applications for cubic congruence equations[J]. AIMS Mathematics, 2022, 7(6): 10671-10680. doi: 10.3934/math.2022595

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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.

References

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