On distribution properties of cubic residues

Hu Jiayuan; Chen Zhuoyu; Hu Jiayuan; Chen Zhuoyu

doi:10.3934/math.2020388

AIMS Mathematics

2020, Volume 5, Issue 6: 6051-6060. doi: 10.3934/math.2020388

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Research article

On distribution properties of cubic residues

Hu Jiayuan ¹,
Chen Zhuoyu ^{2
,
,}

1.
Department of Mathematics and Computer Science, Hetao College, Bayannur, P. R. China
2.
School of Mathematics, Northwest University, Xi’an, Shaanxi, P. R. China

Received: 09 April 2020 Accepted: 15 July 2020 Published: 23 July 2020
MSC : 11A15, 11L40

In this paper, we use the elementary methods, the properties of the Gauss sums and the estimate for character sums to study the calculating problems of a certain cubic residues modulo p, and give some interesting identities and asymptotic formulas for their counting functions.
- cubic residues,
- third-order character,
- Gauss sums,
- identity,
- asymptotic formula
Citation: Hu Jiayuan, Chen Zhuoyu. On distribution properties of cubic residues[J]. AIMS Mathematics, 2020, 5(6): 6051-6060. doi: 10.3934/math.2020388

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Abstract

In this paper, we use the elementary methods, the properties of the Gauss sums and the estimate for character sums to study the calculating problems of a certain cubic residues modulo p, and give some interesting identities and asymptotic formulas for their counting functions.

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