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 The hybrid mean value of Dedekind sums and two-term exponential sums

2016 ◽  
Vol 14 (1) ◽  
pp. 436-442
Author(s):  
Chang Leran ◽  
Li Xiaoxue
Keyword(s):  
Asymptotic Formula ◽  
Exponential Sums ◽  
Mean Value ◽  
Gauss Sums ◽  
Mean Value Theorem ◽  
Dedekind Sums ◽  
Hybrid Mean Value ◽  
The Mean ◽  
Interesting Identity

AbstractIn this paper, we use the mean value theorem of Dirichlet L-functions, the properties of Gauss sums and Dedekind sums to study the hybrid mean value problem involving Dedekind sums and the two-term exponential sums, and give an interesting identity and asymptotic formula for it.

scholarly journals A Hybrid Mean Value Involving Dedekind Sums and the General Exponential Sums

2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
Jianghua Li ◽  
Tingting Wang
Keyword(s):  
Asymptotic Formula ◽  
Upper Bound ◽  
Exponential Sums ◽  
Mean Value ◽  
Gauss Sums ◽  
Dedekind Sums ◽  
Analytic Method ◽  
Hybrid Mean Value ◽  
Classical Work ◽  
Upper Bound Estimate

The main purpose of this paper is using the analytic method, A. Weil’s classical work for the upper bound estimate of the general exponential sums, and the properties of Gauss sums to study the hybrid mean value problem involving Dedekind sums and the general exponential sums and give a sharp asymptotic formula for it.

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 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.

scholarly journals A Hybrid Mean Value Involving the Two-Term Exponential Sums and Two-Term Character Sums

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Liu Miaohua ◽  
Li Xiaoxue
Keyword(s):  
Asymptotic Formula ◽  
Exponential Sums ◽  
Character Sums ◽  
Mean Value ◽  
Gauss Sums ◽  
Hybrid Mean Value

The main purpose of this paper is using the properties of Gauss sums and the estimate for character sums to study the hybrid mean value problem involving the two-term exponential sums and two-term character sums and give an interesting asymptotic formula for it.

scholarly journals A Hybrid Mean Value Involving Dedekind Sums and the Generalized Kloosterman Sums

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Xiaowei Pan ◽  
Xiaoyan Guo
Keyword(s):  
Mean Value ◽  
Gauss Sums ◽  
Kloosterman Sums ◽  
Mean Value Theorem ◽  
Dedekind Sums ◽  
Hybrid Mean Value ◽  
The Mean ◽  
Interesting Identity

In this paper, we use the mean value theorem of Dirichlet L -functions and the properties of Gauss sums and Dedekind sums to study the hybrid mean value problem involving Dedekind sums and the general Kloosterman sums and give an interesting identity for it.

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 Mean Value Involving Kloosterman Sums and Sums Analogous to Dedekind Sums

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Di Han ◽  
Wenpeng Zhang
Keyword(s):  
Mean Value ◽  
Gauss Sums ◽  
Kloosterman Sums ◽  
Mean Value Theorem ◽  
Dedekind Sums ◽  
Hybrid Mean Value ◽  
The Mean

The main purpose of this paper is using the properties of Gauss sums and the mean value theorem of DirichletL-functions to study one kind of hybrid mean value problems involving Kloosterman sums and sums analogous to Dedekind sums and give two exact computational formulae 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.

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