scholarly journals On the Sixth Power Mean Value of the Generalized Three-Term Exponential Sums

2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
Yahui Yu ◽  
Wenpeng Zhang
Keyword(s):  
Exponential Sums ◽  
Mean Value ◽  
Computational Formula ◽  
Power Mean ◽  
Trigonometric Sums ◽  
Computational Problem

The main purpose of this paper is using the estimate for trigonometric sums and the properties of the congruence equations to study the computational problem of one kind sixth power mean value of the generalized three-term exponential sums and give an exact computational formula for it.

scholarly journals One kind sixth power mean of the three-term exponential sums

2017 ◽  
Vol 15 (1) ◽  
pp. 705-710 ◽  
Author(s):  
Xiaoying Wang ◽  
Xiaoxue Li
Keyword(s):  
Exponential Sums ◽  
Computational Formula ◽  
Power Mean ◽  
Trigonometric Sums ◽  
Computational Problem

Abstract In this paper, we use the estimate for trigonometric sums and the properties of the congruence equations to study the computational problem of one kind sixth power mean of the three-term exponential sums. As a conclusion, we give an exact computational formula for it.

scholarly journals On the General Dedekind Sums and Two-Term Exponential Sums

2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
Junli Zhang ◽  
Wenpeng Zhang
Keyword(s):  
Exponential Sums ◽  
Mean Value ◽  
Gauss Sums ◽  
Dedekind Sums ◽  
Computational Formula ◽  
Computational Problem ◽  
Hybrid Mean Value ◽  
Analytic Methods

We use the analytic methods and the properties of Gauss sums to study the computational problem of one kind hybrid mean value involving the general Dedekind sums and the two-term exponential sums, and give an interesting computational formula for it.

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 New Mixed Exponential Sums and Their Application

2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
Yu Zhan ◽  
Xiaoxue Li
Keyword(s):  
Asymptotic Formula ◽  
Upper Bound ◽  
Exponential Sums ◽  
Mean Value ◽  
Fourth Power ◽  
Computational Formula ◽  
Power Mean ◽  
Fourth Power Mean ◽  
Upper Bound Estimate ◽  
The Mean

The main purpose of this paper is to introduce a new mixed exponential sums and then use the analytic methods and the properties of Gauss sums to study the computational problems of the mean value involving these sums and give an interesting computational formula and a sharp upper bound estimate for these mixed exponential sums. As an application, we give a new asymptotic formula for the fourth power mean of DirichletL-functions with the weight of these mixed exponential sums.

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 On the Fourth Power Mean of the Two-Term Exponential Sums

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Han Zhang ◽  
Wenpeng Zhang
Keyword(s):  
Asymptotic Formula ◽  
Exponential Sums ◽  
Gauss Sums ◽  
Fourth Power ◽  
Power Mean ◽  
Computational Problem ◽  
Analytic Methods ◽  
Fourth Power Mean ◽  
Interesting Identity

The main purpose of this paper is to use the analytic methods and the properties of Gauss sums to study the computational problem of one kind fourth power mean of two-term exponential sums and give an interesting identity and asymptotic formula for it.

On the mean value of mixed exponential sums

2016 ◽  
Vol 13 (06) ◽  
pp. 1515-1530
Author(s):  
Ming-Liang Gong ◽  
Ya-Li Li
Keyword(s):  
Explicit Formula ◽  
Exponential Sums ◽  
Dirichlet Character ◽  
Mean Value ◽  
Fourth Power ◽  
Power Mean ◽  
Analytic Methods ◽  
Fourth Power Mean ◽  
The Mean

We use analytic methods to obtain an explicit formula for the fourth power mean [Formula: see text] where [Formula: see text], [Formula: see text] is a Dirichlet character modulo [Formula: see text] and [Formula: see text] denotes the summation over all [Formula: see text] such that [Formula: see text]. This extends the result of Chen, Ai and Cai by overcoming the limitation [Formula: see text].

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 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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