scholarly journals On the High-Power Mean of the Generalized Gauss Sums and Kloosterman Sums

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 907 ◽  
Author(s):  
Xinyu Liu ◽  
Wenpeng Zhang
Keyword(s):  
High Power ◽  
Character Sums ◽  
Gauss Sums ◽  
Kloosterman Sums ◽  
Power Mean ◽  
Trigonometric Sums ◽  
Computational Problem

The main aim of this paper is to use the properties of the trigonometric sums and character sums, and the number of the solutions of several symmetry congruence equations to research the computational problem of a certain sixth power mean of the generalized Gauss sums and generalized Kloosterman sums, and to give two exact computational formulae for them.

scholarly journals One kind power mean of the hybrid Gauss sums

2018 ◽  
Vol 16 (1) ◽  
pp. 531-538
Author(s):  
Qi Lan ◽  
Zhang Wenpeng
Keyword(s):  
Exact Formula ◽  
Gauss Sums ◽  
Computational Formula ◽  
Analysis Method ◽  
Power Mean ◽  
Trigonometric Sums ◽  
Number Of Solutions ◽  
Computational Problem ◽  
Congruence Equation

AbstractIn this paper, we use the analysis method and the properties of trigonometric sums to study the computational problem of one kind power mean of the hybrid Gauss sums. After establishing some relevant lemmas, we give an exact computational formula for it. As an application of our result, we give an exact formula for the number of solutions of one kind diagonal congruence equation modp, wherepbe an odd prime.

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 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.

A new identity involving the classical Kloosterman sums and 2-dimensional Kloosterman sums

2016 ◽  
Vol 12 (01) ◽  
pp. 111-119 ◽  
Author(s):  
Wenpeng Zhang ◽  
Di Han
Keyword(s):  
Gauss Sums ◽  
Kloosterman Sums ◽  
Fourth Power ◽  
Power Mean ◽  
Trigonometric Sums ◽  
Fourth Power Mean ◽  
Interesting Identity

The main purpose of this paper is, using the properties of Gauss sums and the estimate for trigonometric sums, to study the relationships between the sixth power mean of the classical Kloosterman sums and the fourth power mean of the 2-dimensional Kloosterman sums, and give an interesting identity for them.

scholarly journals On the character sums analogous to high dimensional Kloosterman sums

2021 ◽  
Vol 7 (1) ◽  
pp. 294-305
Author(s):  
Jianghua Li ◽  
◽  
Xi Zhang
Keyword(s):  
Character Sums ◽  
Gauss Sums ◽  
Kloosterman Sums ◽  
High Dimensional ◽  
Computational Problem ◽  
Analytic Methods

<abstract><p>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 character sums analogous to high dimensional Kloosterman sums, and give some interesting identities for it.</p></abstract>

scholarly journals On the hybrid power mean of two kind different trigonometric sums

2019 ◽  
Vol 17 (1) ◽  
pp. 519-526
Author(s):  
Chen Zhuoyu ◽  
Zhang Wenpeng
Keyword(s):  
Gauss Sums ◽  
Analytic Method ◽  
Computational Formula ◽  
Power Mean ◽  
Trigonometric Sums ◽  
Computational Problem ◽  
Hybrid Power ◽  
Hybrid Power Mean

Abstract The main purpose of this paper is using the analytic method, the properties of trigonometric sums and Gauss sums to study the computational problem of one kind hybrid power mean involving two different trigonometric sums, and give an interesting computational formula for it.

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

2021 ◽  
Vol 27 (1) ◽  
pp. 112-124
Author(s):  
Xiaoling Xu ◽  
◽  
Jiafan Zhang ◽  
Wenpeng Zhang ◽  
◽  
...  
Keyword(s):  
Asymptotic Formula ◽  
Exponential Sums ◽  
Character Sums ◽  
Gauss Sums ◽  
Character Sum ◽  
Power Mean ◽  
Computational Problem ◽  
Hybrid Power ◽  
Analytic Methods ◽  
Hybrid Power Mean

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.

scholarly journals On Classical Gauss Sums and Some of Their Properties

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 625 ◽  
Author(s):  
Li Chen
Keyword(s):  
Recursive Formula ◽  
Character Sums ◽  
Gauss Sums ◽  
Computational Problem ◽  
Rational Polynomials

The goal of this paper is to solve the computational problem of one kind rational polynomials of classical Gauss sums, applying the analytic means and the properties of the character sums. Finally, we will calculate a meaningful recursive formula for it.

scholarly journals The generalized quadratic Gauss sums and its sixth power mean

2021 ◽  
Vol 6 (10) ◽  
pp. 11275-11285
Author(s):  
Xingxing Lv ◽  
◽  
Wenpeng Zhang
Keyword(s):  
Gauss Sums ◽  
Power Mean ◽  
Computational Problem ◽  
Elementary Methods

<abstract><p>In this article, we using elementary methods, the number of the solutions of some congruence equations and the properties of the Legendre's symbol to study the computational problem of the sixth power mean of a certain generalized quadratic Gauss sums, and to give an exact calculating formula for it.</p></abstract>

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