Results 11 to 20 of about 2,373,714 (282)

On the Fourth Power Mean of the Two-Term Exponential Sums [PDF]

The Scientific World Journal, 2014
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.
Han Zhang, Wenpeng Zhang
doaj   +6 more sources

A new fourth power mean of two-term exponential sums [PDF]

Open Mathematics, 2019
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.
Li Chen, Xiao Wang
doaj   +6 more sources

The Generalized Quadratic Gauss Sum and Its Fourth Power Mean [PDF]

Mathematics, 2019
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 ...
Shimeng Shen, Wenpeng Zhang
doaj   +5 more sources

One special kind of Kloosterman sum and its fourth-power mean

Open Mathematics
This article aims to investigate the calculation problem of the fourth-power mean of the specific Kloosterman sums by utilizing analytic methods and the properties of classical Gauss sums.
Zhang Wenpeng, Wang Li, Liu Xiaoge
doaj   +5 more sources

A New Sum Analogous to Gauss Sums and Its Fourth Power Mean [PDF]

The Scientific World Journal, 2014
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 ...
Shaofeng Ru, Wenpeng Zhang
doaj   +5 more sources

On the generalized exponential sums and their fourth power mean

Open Mathematics
The main purpose of this article is to study the calculating problem of the fourth power mean of the two-term exponential sums and provide an accurate calculating formula for utilizing analytical methods and character sums’ properties. In the meantime, a
Liu Wencong, Ning Shushu
doaj   +4 more sources

On the Fourth Hybrid Power Mean Involving the Generalized Gauss Sums

Journal of Mathematics, 2023
In this paper, we use the elementary and analytic methods to study the fourth hybrid power mean involving the generalized Gauss sums and prove several interesting identities for them.
Xiaoge Liu, Yuanyuan Meng
doaj   +3 more sources

On the general Kloosterman sum and its fourth power mean

Journal of Number Theory, 2004
Let \(q \geq 3\) be a positive integer and let \(\chi\) denote a Dirichlet character mod \(q\). For any integers \(m\) and \(n\), the general Kloosterman sum \(S(m ,n , \chi ; q)\) is defined as follows: \[ S(m,n, \chi ; q) = \mathop{{\sum}^*}_{a=1}^q \chi(a) e\left(\frac {ma+n \overline{a}}{q} \right), \] where \(e(y) = e^{2 \pi i y}\) and \(\sum ...
Wenpeng Zhang
semanticscholar   +5 more sources

On the general Gauss sums and their fourth power mean [PDF]

, 2005
Lfeing the elementary method the calculating problem of the fourth power mean of the general k-th Gauss sums is studied,and an exact calculating formula is given.
Wenpeng Zhang, Huan Liu
semanticscholar   +8 more sources

The Fourth Hybrid Power Mean Involving the Character Sums and Exponential Sums

Mathematics
In this paper, we consider the fourth hybrid power mean involving two-term exponential sums and third-order character sum modulo p, a topic of significant importance in analytic number theory.
Guohui Chen, Tingting Du
doaj   +3 more sources