The hybrid power mean of some special character sums of polynomials and two-term exponential sums modulo $ p $

Wenpeng Zhang; Jiafan Zhang; Wenpeng Zhang; Jiafan Zhang

doi:10.3934/math.2021638

AIMS Mathematics

2021, Volume 6, Issue 10: 10989-11004. doi: 10.3934/math.2021638

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The hybrid power mean of some special character sums of polynomials and two-term exponential sums modulo $ p $

Wenpeng Zhang ¹,
Jiafan Zhang ^{2
,
,}

1.
School of Science, Xi'an Technological University, Xi'an, Shaanxi, China
2.
School of Mathematics, Northwest University, Xi'an, Shaanxi, China

Received: 10 April 2021 Accepted: 18 July 2021 Published: 29 July 2021
MSC : 11L03, 11L40

We consider the calculation problem of one kind hybrid power mean involving the character sums of polynomials and two-term exponential sums modulo $ p $, an odd prime, and use the analytic method and the properties of classical Gauss sums to give some identities and asymptotic formulas for them.
- the character sums of polynomials,
- two-term exponential sums,
- hybrid power mean,
- analytic method,
- identity,
- asymptotic formula
Citation: Wenpeng Zhang, Jiafan Zhang. The hybrid power mean of some special character sums of polynomials and two-term exponential sums modulo $ p $[J]. AIMS Mathematics, 2021, 6(10): 10989-11004. doi: 10.3934/math.2021638

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Abstract

We consider the calculation problem of one kind hybrid power mean involving the character sums of polynomials and two-term exponential sums modulo $ p $, an odd prime, and use the analytic method and the properties of classical Gauss sums to give some identities and asymptotic formulas for them.

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