A new identity involving the classical Kloosterman sums and 2-dimensional Kloosterman sums

2016 ◽  
Vol 12 (01) ◽  
pp. 111-119 ◽  
Author(s):  
Wenpeng Zhang ◽  
Di Han
Keyword(s):  
Gauss Sums ◽  
Kloosterman Sums ◽  
Fourth Power ◽  
Power Mean ◽  
Trigonometric Sums ◽  
Fourth Power Mean ◽  
Interesting Identity

The main purpose of this paper is, using the properties of Gauss sums and the estimate for trigonometric sums, to study the relationships between the sixth power mean of the classical Kloosterman sums and the fourth power mean of the 2-dimensional Kloosterman sums, and give an interesting identity for them.

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 The Generalized Quadratic Gauss Sum and Its Fourth Power Mean

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 258
Author(s):  
Shimeng Shen ◽  
Wenpeng Zhang
Keyword(s):  
Character Sums ◽  
Gauss Sums ◽  
Gauss Sum ◽  
Fourth Power ◽  
Power Mean ◽  
Analytic Methods ◽  
Fourth Power Mean

In this article, our main purpose is to introduce a new and generalized quadratic Gauss sum. By using analytic methods, the properties of classical Gauss sums, and character sums, we consider the calculating problem of its fourth power mean and give two interesting computational formulae for it.

On the hyper-Kloosterman sum and its fourth power mean

2009 ◽  
Vol 46 (4) ◽  
pp. 479-492
Author(s):  
Zhefeng Xu
Keyword(s):  
Kloosterman Sums ◽  
Fourth Power ◽  
Kloosterman Sum ◽  
Power Mean ◽  
Fourth Power Mean

The main purpose of this paper is to study the calculating problem of the fourth power mean of the hyper-Kloosterman sums, and give an exact calculating formula for them.

scholarly journals Dirichlet characters of the rational polynomials

2021 ◽  
Vol 7 (3) ◽  
pp. 3494-3508
Author(s):  
Wenjia Guo ◽  
◽  
Xiaoge Liu ◽  
Tianping Zhang
Keyword(s):  
Dirichlet Character ◽  
Character Sums ◽  
Gauss Sums ◽  
Fourth Power ◽  
Power Mean ◽  
Dirichlet Characters ◽  
Fourth Power Mean ◽  
Rational Polynomials

<abstract><p>Denote by $ \chi $ a Dirichlet character modulo $ q\geq 3 $, and $ \overline{a} $ means $ a\cdot\overline{a} \equiv 1 \bmod q $. In this paper, we study Dirichlet characters of the rational polynomials in the form</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \sum\limits^{q}_{a = 1}'\chi(ma+\overline{a}), $\end{document} </tex-math></disp-formula></p> <p>where $ \sum\limits_{a = 1}^{q}' $ denotes the summation over all $ 1\le a\le q $ with $ (a, q) = 1 $. Relying on the properties of character sums and Gauss sums, we obtain W. P. Zhang and T. T. Wang's identity <sup>[<xref ref-type="bibr" rid="b6">6</xref>]</sup> under a more relaxed situation. We also derive some new identities for the fourth power mean of it by adding some new ingredients.</p></abstract>

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 On the fourth power mean of the general k th Kloosterman sums

2014 ◽  
Vol 2014 (1) ◽  
Author(s):  
Xiaoyan Guo ◽  
Guohua Geng ◽  
Xiaowei Pan
Keyword(s):  
Kloosterman Sums ◽  
Fourth Power ◽  
Power Mean ◽  
Fourth Power Mean
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