Results 211 to 219 of about 138,517 (219)

The mean value involving Dedekind sums and two-term exponential sums

Science China Mathematics, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wang, Tingting, Pan, Xiaowei
exaly   +3 more sources

ON THE THIRD POWER MEAN OF TWO-TERM EXPONENTIAL SUMS

JP Journal of Algebra, Number Theory and Applications
Using the properties of character sums and the classical Gauss sums, we study the computational problem of one kind of third power mean of the two-term exponential sums, and give an exact computational formula.
Cui, Dewang, Wang, Li
openaire   +2 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.
exaly   +2 more sources

THE HYBRID POWER MOMENT OF CHARACTER SUMS AND TWO-TERM EXPONENTIAL SUMS

JP Journal of Algebra, Number Theory and Applications
This paper focuses on the investigation of the hybrid power mean concerning some special character sums of polynomials and the two-term exponential sums by utilizing analytical approaches and the nature of Gauss sums to give two sharp asymptotic formulae for them.
openaire   +2 more sources

ON TWO-TERM EXPONENTIAL SUMS AND A NEW FIFTH POWER MEAN

JP Journal of Algebra, Number Theory and Applications
The primary aim of this paper is to study the problem of a new fifth power mean of the two-term exponential sums. By employing elementary methods, the number of solutions to a few congruence equations is obtained. Besides certain properties of classical Gauss sums have been derived.
openaire   +2 more sources

On the hybrid mean value of two-term exponential sums and character sums of polynomials

Lithuanian Mathematical Journal
For \(q,m,n,u,v\) positive integers with \(q\geq 3\) and \(u>v\), the two term exponential sums of \(u\) degree is defined by \[ C(m, n, u, v; q) := \sum_{\substack{a=1 \\ (a,q)=1}}^{q} e\left(\frac{ma^u + na^v}{q}\right). \] With \(M,N\) positive integers, \(\chi\) any Dirichlet character modulo \(q\), and \(f\) a polynomial (over \(\mathbb{Z}\)), the
Sun, Zhangrui, Han, Di
exaly   +3 more sources

A HIGH-ORDER TWO-TERM EXPONENTIAL SUM AND ITS MEAN VALUE PROBLEM

JP Journal of Algebra, Number Theory and Applications
Summary: This paper investigates a high-order two-term exponential sum and its mean value problem. The main focus is on studying the calculation problem of the fourth power mean of the high-order two-term exponential sum. This is done by utilizing the number of solutions of congruence equations and analytic methods.
Wang, Li, Liu, Xiaoge
openaire   +2 more sources

A note on fourth power mean of the general two-term exponential sums

Mathematical Reports
Let $q$, $m$, $n$ be any integer with $q\ge 3$, and $\lambda$ a Dirichlet character $\bmod $ $q$. An explicit formula for the fourth power mean $$ \mathop{\sum}_{{m=1}\atop{(m,q)=1}}^{q} \biggl| \mathop{\sum}_{a=1}^{q} \lambda(a) e\biggl( \frac{ma^3+na}{q} \biggr) \biggr|^4 $$ is derived.
Mu, Yaya, Zhang, Tianping
openaire   +2 more sources

One kind sixth power mean of the three-term exponential sums

Open Mathematics, 2017
exaly