scholarly journals The hybrid power mean of the generalized Gauss sums

2017 ◽  
Vol 2017 (1) ◽  
Author(s):  
Li Chen ◽  
Wenpeng Zhang
Keyword(s):  
Gauss Sums ◽  
Power Mean ◽  
Hybrid Power ◽  
Hybrid Power Mean

scholarly journals A note on two-term exponential sum and the reciprocal of the quartic Gauss sums

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Wenpeng Zhang ◽  
Xingxing Lv
Keyword(s):  
Exponential Sums ◽  
Exponential Sum ◽  
Gauss Sums ◽  
Power Mean ◽  
Hybrid Power ◽  
Analytic Methods ◽  
Hybrid Power Mean

AbstractThe main purpose of this article is by using the properties of the fourth character modulo a prime p and the analytic methods to study the calculating problem of a certain hybrid power mean involving the two-term exponential sums and the reciprocal of quartic Gauss sums, and to give some interesting calculating formulae of them.

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

2021 ◽  
Vol 6 (10) ◽  
pp. 10989-11004
Author(s):  
Wenpeng Zhang ◽  
◽  
Jiafan Zhang ◽  
Keyword(s):  
Exponential Sums ◽  
Character Sums ◽  
Gauss Sums ◽  
Asymptotic Formulas ◽  
Analytic Method ◽  
Power Mean ◽  
Hybrid Power ◽  
Special Character ◽  
Modulo P ◽  
Hybrid Power Mean

<abstract><p>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.</p></abstract>

scholarly journals On the two-term exponential sums and character sums of polynomials

2019 ◽  
Vol 17 (1) ◽  
pp. 1239-1248
Author(s):  
Yuankui Ma ◽  
Wenpeng Zhang
Keyword(s):  
Exponential Sums ◽  
Character Sums ◽  
Gauss Sums ◽  
Asymptotic Formulas ◽  
Power Mean ◽  
Computational Problem ◽  
Hybrid Power ◽  
Analytic Methods ◽  
Hybrid Power Mean

Abstract The main aim of this paper is to use the analytic methods and the properties of the classical Gauss sums to research the computational problem of one kind hybrid power mean containing the character sums of polynomials and two-term exponential sums modulo p, an odd prime, and acquire several accurate asymptotic formulas for them.

scholarly journals A Hybrid Power Mean Involving the Dedekind Sums and Cubic Gauss Sums

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Jiayuan Hu ◽  
Yu Zhan ◽  
Qin Si
Keyword(s):  
Gauss Sums ◽  
Gauss Sum ◽  
Dedekind Sums ◽  
Power Mean ◽  
Hybrid Power ◽  
Analytic Methods ◽  
Hybrid Power Mean

The main purpose of this paper is using analytic methods and the properties of the Dedekind sums to study one kind hybrid power mean calculating problem involving the Dedekind sums and cubic Gauss sum and give some interesting calculating formulae for it.

scholarly journals On the Hybrid Power Mean Involving the Character Sums and Dedekind Sums

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Xiaoling Xu
Keyword(s):  
Character Sums ◽  
Gauss Sums ◽  
Dedekind Sums ◽  
Character Sum ◽  
Kloosterman Sum ◽  
Power Mean ◽  
Computational Problem ◽  
Hybrid Power ◽  
Analytic Methods ◽  
Hybrid Power Mean

The main purpose of this paper is to use the elementary and analytic methods, the properties of Gauss sums, and character sums to study the computational problem of a certain hybrid power mean involving the Dedekind sums and a character sum analogous to Kloosterman sum and give two interesting identities for them.

scholarly journals The hybrid power mean of quartic Gauss sums and Kloosterman sums

2017 ◽  
Vol 15 (1) ◽  
pp. 151-156 ◽  
Author(s):  
Li Xiaoxue ◽  
Hu Jiayuan
Keyword(s):  
Gauss Sums ◽  
Kloosterman Sums ◽  
Analytic Method ◽  
Computational Formula ◽  
Power Mean ◽  
Computational Problem ◽  
Hybrid Power ◽  
Hybrid Power Mean

Abstract The main purpose of this paper is using the analytic method and the properties of the classical Gauss sums to study the computational problem of one kind fourth hybrid power mean of the quartic Gauss sums and Kloosterman sums, and give an exact computational formula for it.

scholarly journals On the recursive properties of one kind hybrid power mean involving two-term exponential sums and Gauss sums

2018 ◽  
Vol 16 (1) ◽  
pp. 955-966
Author(s):  
Shimeng Shen
Keyword(s):  
Exponential Sums ◽  
Gauss Sums ◽  
Linear Recurrence ◽  
Analytic Method ◽  
Computational Formula ◽  
Power Mean ◽  
Hybrid Power ◽  
Recurrence Formulae ◽  
Hybrid Power Mean ◽  
Congruence Equation

AbstractThe main purpose of this paper is to study the computational problem of one kind hybrid power mean involving two-term exponential sums and quartic Gauss sums using the analytic method and the properties of the classical Gauss sums, and to prove some interesting fourth-order linear recurrence formulae for this problem. As an application of our result, we can also obtain an exact computational formula for one kind congruence equation modp, an odd prime.

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