On the Hybrid Mean Value Involving Dedekind Sums and Kloosterman Sums

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.

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

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 2079
Author(s):  
Lei Liu ◽  
Zhefeng Xu
Keyword(s):  
Character Sums ◽  
Mean Value ◽  
Dedekind Sums ◽  
Hybrid Mean Value ◽  
Asymptotic Formulae ◽  
The Mean

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.

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 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 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 asymptotic properties of the generalized Dirichlet L-functions

2019 ◽  
Vol 15 (06) ◽  
pp. 1305-1321
Author(s):  
Rong Ma ◽  
Yana Niu ◽  
Yulong Zhang
Keyword(s):  
Real Number ◽  
Analytic Continuation ◽  
Asymptotic Properties ◽  
Dirichlet Character ◽  
Mean Value ◽  
Analytic Method ◽  
Asymptotic Formulae ◽  
Number Formula ◽  
The Mean ◽  
Generalized Dirichlet

Let [Formula: see text] be an integer, [Formula: see text] denote a Dirichlet character modulo [Formula: see text], for any real number [Formula: see text], we define the generalized Dirichlet [Formula: see text]-functions [Formula: see text] where [Formula: see text] with [Formula: see text] and [Formula: see text] both real. It can be extended to all [Formula: see text] by analytic continuation. In this paper, we study the mean value properties of the generalized Dirichlet [Formula: see text]-functions, and obtain several sharp asymptotic formulae by using analytic method.

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