Results 11 to 20 of about 9,452,959 (273)

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   +4 more sources

ON THE FOURTH POWER MEAN OF TWO-TERM EXPONENTIAL SUMS

JP Journal of Algebra, Number Theory and Applications
Using elementary methods and character sum estimates, we study the fourth power mean of two-term exponential sums with exponent seven, and obtain a sharp asymptotic formula, extending existing results for exponent 5 to exponent 7 clarifying the asymptotic behavior for general odd primes.
Wencong Liu
semanticscholar   +3 more sources

ON THE FOURTH POWER MEAN OF GENERALIZED TWO-TERM EXPONENTIAL SUMS [PDF]

Bulletin of the Korean Mathematical Society, 2013
In this paper, we use the elementary method and the theory of complex functions to study the computational problem of the fourth power mean of the generalized two-term exponential sums, and give two exact identities for them.
Ting-Ting Wang
exaly   +3 more sources

The fourth and sixth power mean of the classical Kloosterman sums [PDF]

Journal of Number Theory, 2011
Let \(S(m,n;q)\) be the classical Kloosterman sums and \(q\geq 3\). The paper obtains: For \((n,q)=1\), then \[ \sum\limits_{m=1}^{q}|S(m,n;q)|^{4}=3^{\omega(q)}q^{2}\varphi(q)\prod\limits_{p\|q}\left(\frac{2}{3}-\frac{1}{3p}-\frac{4}{3p(p-1)}\right), \] where \(\omega(q)\) denotes the number of all different prime divisors of \(q\) and \(\varphi(q ...
Wenpeng Zhang
exaly   +3 more sources

Generalized polynomial exponential sums and their fourth power mean

Electronic Research Archive, 2023
<abstract><p>The study of the power mean of the generalized polynomial exponential sums plays a very important role in analytic number theory, and many classical number theory problems are closely related to it. In this article, we use the elementary methods and the properties of the exponential sums to study the calculating problem of one ...
Li Wang, Yuanyuan Meng
openaire   +3 more sources

On the Hybrid Fourth Power Mean Involving Legendre’s Symbol and One Kind Two-Term Exponential Sums

Journal of Mathematics, 2021
The main purpose of this article is using the elementary methods and the properties of the quadratic residue modulo an odd prime p to study the calculating problem of the fourth power mean of one kind two-term exponential sums and give an interesting ...
Jingzhe Wang
doaj   +2 more sources

The generalized Kloosterman's sums and its fourth power mean

AIMS Mathematics, 2023
<abstract><p>The main purpose of this article is to study the calculating problem of one kind fourth power mean of the generalized Kloosterman's sums and provide an accurate calculating formula for it utilizing analytical methods and character sums' properties.
Junfeng Cui, Li Wang
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The fourth power mean of Dirichlet L-functions in $${\mathbb {F}}_q [T]$$ [PDF]

Revista Matemática Complutense, 2020
AbstractWe prove results on moments of L-functions in the function field setting, where the moment averages are taken over primitive characters of modulus R, where R is a polynomial in $${\mathbb {F}}_{q}[T]$$ F q
Julio Cesar Andrade, Michael Yiasemides
semanticscholar   +6 more sources

Fourth power mean values of one kind special Kloosterman's sum

Electronic Research Archive, 2023
<abstract><p>The main purpose of this article is using the analytic methods and properties of classical Gauss sums to study the calculating problem of fourth power mean values of one kind special Kloosterman's sum, and give a sharp asymptotic formula for it.
Li Rui, Nilanjan Bag
openaire   +4 more sources

On the fourth power mean of the general k th Kloosterman sums [PDF]

Advances in Difference Equations, 2014
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Guo, Xiaoyan, Geng, Guohua, Pan, Xiaowei
openaire   +3 more sources