A sum analogous to Kloosterman sum and its fourth power mean

He Yanqin; Zhu Chaoxi; Chen Zhuoyu; He Yanqin; Zhu Chaoxi; Chen Zhuoyu

doi:10.3934/math.2020168

AIMS Mathematics

2020, Volume 5, Issue 3: 2569-2576. doi: 10.3934/math.2020168

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Research article

A sum analogous to Kloosterman sum and its fourth power mean

1.
Department of Basic Education, Shaanxi Fashion Engineering University, Xi’an, Shaanxi, P. R. China
2.
Mathematical College, Sichuan University, Chengdu, SiChuan, P. R. China
3.
School of Mathematics, Northwest University, Xi’an, Shaanxi, P. R. China

Received: 29 October 2019 Accepted: 05 March 2020 Published: 11 March 2020
MSC : 11L03, 11L05

The main purpose of this paper is using the analytic methods and the properties of the Legendre's symbol and quadratic residue mod p to study the computational problem of the fourth power mean of a sum analogous to Kloosterman sum, and give a sharp asymptotic formula for it.
- a sum analogous to Kloosterman sum,
- the fourth power mean,
- asymptotic formula,
- analytic method
Citation: He Yanqin, Zhu Chaoxi, Chen Zhuoyu. A sum analogous to Kloosterman sum and its fourth power mean[J]. AIMS Mathematics, 2020, 5(3): 2569-2576. doi: 10.3934/math.2020168

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Abstract

The main purpose of this paper is using the analytic methods and the properties of the Legendre's symbol and quadratic residue mod p to study the computational problem of the fourth power mean of a sum analogous to Kloosterman sum, and give a sharp asymptotic formula for it.

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