The character sum of polynomials with k variables and two-term exponential sums

Xu Xiaoling, Zhang Jiafan and Zhang Wenpeng
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 27, 2021, Number 1, Pages 112–124
DOI: 10.7546/nntdm.2021.27.1.112-124
Full paper (PDF, 201 Kb)

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Authors and affiliations

Xu Xiaoling
School of Data Science and Engineering, Xi’an Innovation College of Yan’an University
Xi’an, Shaanxi, P. R. China

Zhang Jiafan
School of Mathematics, Northwest University
Xi’an, Shaanxi, P. R. China

Zhang Wenpeng
School of Mathematics, Northwest University
Xi’an, Shaanxi, P. R. China

Abstract

The main purpose of this paper is using the properties of the classical Gauss sums and the analytic methods to study the computational problem of one kind of hybrid power mean involving the character sums of polynomials with k variables and the two-term exponential sums, and give an identity and asymptotic formula for it.

Keywords

• Character sums of polynomials with k variables
• Two-term exponential sums
• Hybrid power mean
• Analytic method
• Identity
• Asymptotic formula

2010 Mathematics Subject Classification

• 11L03
• 11L40

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