scholarly journals Fourth power mean of character sums

2008 ◽  
Vol 135 (1) ◽  
pp. 31-49 ◽  
Author(s):  
Zhefeng Xu ◽  
Wenpeng Zhang
Keyword(s):  
Character Sums ◽  
Fourth Power ◽  
Power Mean ◽  
Fourth Power Mean

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.

On the Fourth Power Mean of the Character Sums Over Short Intervals

2006 ◽  
Vol 23 (1) ◽  
pp. 153-164 ◽  
Author(s):  
Wen Peng Zhang ◽  
Xiao Ying Wang
Keyword(s):  
Character Sums ◽  
Fourth Power ◽  
Power Mean ◽  
Short Intervals ◽  
Fourth Power Mean

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.

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>

ON THE GENERAL k-TH KLOOSTERMAN SUMS AND ITS FOURTH POWER MEAN

2004 ◽  
Vol 25 (01) ◽  
pp. 97-102 ◽  
Author(s):  
HONGYAN LIU ◽  
WENPENG ZHANG
Keyword(s):  
Kloosterman Sums ◽  
Fourth Power ◽  
Power Mean ◽  
Fourth Power Mean

scholarly journals On the fourth power mean of the analogous general Kloosterman sum

2016 ◽  
Vol 160 ◽  
pp. 326-333 ◽  
Author(s):  
Hui Chen ◽  
Tianping Zhang
Keyword(s):  
Fourth Power ◽  
Kloosterman Sum ◽  
Power Mean ◽  
Fourth Power Mean

scholarly journals A note on the fourth power mean of the generalized Kloosterman sums

2017 ◽  
Vol 174 ◽  
pp. 419-426 ◽  
Author(s):  
Wenpeng Zhang ◽  
Shimeng Shen
Keyword(s):  
Kloosterman Sums ◽  
Fourth Power ◽  
Power Mean ◽  
Fourth Power Mean

scholarly journals A certain new Gauss sum and its fourth power mean

2020 ◽  
Vol 5 (5) ◽  
pp. 5004-5011
Author(s):  
Yan Zhao ◽  
◽  
Wenpeng Zhang ◽  
Xingxing Lv ◽  
Keyword(s):  
Gauss Sum ◽  
Fourth Power ◽  
Power Mean ◽  
Fourth Power Mean
Sign in / Sign up

Export Citation Format

Share Document