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.

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 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 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 A new fourth power mean of two-term exponential sums

2019 ◽  
Vol 17 (1) ◽  
pp. 407-414
Author(s):  
Chen Li ◽  
Wang Xiao
Keyword(s):  
Asymptotic Formula ◽  
Exponential Sums ◽  
Gauss Sums ◽  
Fourth Power ◽  
Power Mean ◽  
Analytic Methods ◽  
Fourth Power Mean

Abstract The main purpose of this paper is to use analytic methods and properties of quartic Gauss sums to study a special fourth power mean of a two-term exponential sums modp, with p an odd prime, and prove interesting new identities. As an application of our results, we also obtain a sharp asymptotic formula for the fourth power mean.

scholarly journals A New Sum Analogous to Gauss Sums and Its Fourth Power Mean

2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
Shaofeng Ru ◽  
Wenpeng Zhang
Keyword(s):  
Upper Bound ◽  
Gauss Sums ◽  
Fourth Power ◽  
Power Mean ◽  
Computational Problem ◽  
Analytic Methods ◽  
Fourth Power Mean ◽  
Upper Bound Estimate

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 of new sum analogous to Gauss sums and give an interesting fourth power mean and a sharp upper bound estimate for it.

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 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 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.

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