scholarly journals ON THE 2k-TH POWER MEAN VALUE OF THE GENERALIZED QUADRATIC GAUSS SUMS

2011 ◽  
Vol 48 (1) ◽  
pp. 9-15 ◽  
Author(s):  
Yanfeng He ◽  
Wenpeng Zhang
Keyword(s):  
Mean Value ◽  
Gauss Sums ◽  
Power Mean

scholarly journals A hybrid mean value of the inversion of L-functions and general quadratic Gauss sums

2002 ◽  
Vol 167 ◽  
pp. 1-15 ◽  
Author(s):  
Wenpeng Zhang ◽  
Yuping Deng
Keyword(s):  
Character Sums ◽  
Mean Value ◽  
Gauss Sums ◽  
Asymptotic Formulas ◽  
Analytic Method ◽  
Power Mean ◽  
Hybrid Mean Value

AbstractThe main purpose of this paper is, using the estimates for character sums and the analytic method, to study the 2k-th power mean of the inversion of Dirichlet L-functions with the weight of general quadratic Gauss sums, and give two interesting asymptotic formulas.

scholarly journals A note on two-term exponential sum and the reciprocal of the quartic Gauss sums

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Wenpeng Zhang ◽  
Xingxing Lv
Keyword(s):  
Exponential Sums ◽  
Exponential Sum ◽  
Gauss Sums ◽  
Power Mean ◽  
Hybrid Power ◽  
Analytic Methods ◽  
Hybrid Power Mean

AbstractThe main purpose of this article is by using the properties of the fourth character modulo a prime p and the analytic methods to study the calculating problem of a certain hybrid power mean involving the two-term exponential sums and the reciprocal of quartic Gauss sums, and to give some interesting calculating formulae of them.

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 The generalized quadratic Gauss sums and its sixth power mean

2021 ◽  
Vol 6 (10) ◽  
pp. 11275-11285
Author(s):  
Xingxing Lv ◽  
◽  
Wenpeng Zhang
Keyword(s):  
Gauss Sums ◽  
Power Mean ◽  
Computational Problem ◽  
Elementary Methods

<abstract><p>In this article, we using elementary methods, the number of the solutions of some congruence equations and the properties of the Legendre's symbol to study the computational problem of the sixth power mean of a certain generalized quadratic Gauss sums, and to give an exact calculating formula for it.</p></abstract>

scholarly journals One Kind Special Gauss Sums and their Mean Square Values

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Jianhong Zhao ◽  
Jiejie Gao
Keyword(s):  
Mean Value ◽  
Gauss Sums ◽  
Mean Square ◽  
Analytic Methods ◽  
The Mean

In this paper, we introduce one kind special Gauss sums; then, using the elementary and analytic methods to study the mean value properties of these kind sums, we obtain several exact calculating formulae for them.

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