Mean Value of the General Dedekind Sums over Interval                                                       \({[1,\frac{q}{p})}\)

Let q>2 be a prime, p be a given prime with p<q. The main purpose of this paper is using transforms, the hybrid mean value of Dirichlet L-functions with character sums and the related properties of character sums to study the mean value of the general Dedekind sums over interval [1,qp), and give some interesting asymptotic formulae.

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

Open Mathematics ◽

10.1515/math-2016-0040 ◽

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.

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

Journal of Mathematics ◽

10.1155/2021/5516217 ◽

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.

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On the Hybrid Mean Value Involving Kloosterman Sums and Sums Analogous to Dedekind Sums

Abstract and Applied Analysis ◽

10.1155/2013/760505 ◽

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.

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On the Hybrid Mean Value Involving Dedekind Sums and Kloosterman Sums

Mathematica Slovaca ◽

10.1515/ms-2015-0034 ◽

2015 ◽

Vol 65 (3) ◽

Author(s):

Ma Rong ◽

Zhang Wenpeng

Keyword(s):

Asymptotic Properties ◽

Dirichlet Character ◽

Mean Value ◽

Kloosterman Sums ◽

Dedekind Sums ◽

Hybrid Mean Value ◽

Analytic Methods ◽

Asymptotic Formulae

AbstractThe main purpose of this paper is using the analytic methods and the estimation of Dirichlet character of polynomials to study the asymptotic properties of one kind hybrid mean value involving the Dedekind sums and Kloosterman sums, and give two interesting asymptotic formulae.

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On the Mean Values of Certain Character Sums

Abstract and Applied Analysis ◽

10.1155/2013/326597 ◽

2013 ◽

Vol 2013 ◽

pp. 1-19

Author(s):

Zhefeng Xu ◽

Huaning Liu

Keyword(s):

Character Sums ◽

Fourth Power ◽

Power Mean ◽

Mean Values ◽

Asymptotic Formulae ◽

Fourth Power Mean ◽

The Mean

Letq≥5be an odd number. In this paper, we study the fourth power mean of certain character sums∑χmodq,χ-1=-1*∑1≤a≤q/4aχa4and∑χmodq,χ-1=1*∑1≤a≤q/4aχa4, where∑‍*denotes the summation over primitive characters moduloq, and give some asymptotic formulae.

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