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

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 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

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 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 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
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