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 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 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.

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 On the Mean Values of Certain Character Sums

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.

scholarly journals On the mean value of L-functions with the weight of character sums

2008 ◽  
Vol 128 (8) ◽  
pp. 2459-2466 ◽  
Author(s):  
Wenpeng Zhang
Keyword(s):  
Character Sums ◽  
Mean Value ◽  
The Mean

scholarly journals On the k-polygonal numbers and the mean value of Dedekind sums

2016 ◽  
Vol 66 (2) ◽  
pp. 409-415
Author(s):  
Jing Guo ◽  
Xiaoxue Li
Keyword(s):  
Mean Value ◽  
Dedekind Sums ◽  
Polygonal Numbers ◽  
The Mean

The hybrid mean value ofL-functions and a special character sums

2014 ◽  
Vol 37 (4) ◽  
pp. 563-570
Author(s):  
Jianghua Li ◽  
Xinqiang Qin ◽  
Fang Zhang
Keyword(s):  
Character Sums ◽  
Mean Value ◽  
Hybrid Mean Value ◽  
Special Character
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