Results 231 to 239 of about 22,813,091 (239)

A new two-term exponential sums and its fourth power mean

Rendiconti del Circolo Matematico di Palermo Series 2, 2023
In the paper under review, the authors prove that for any odd prime \(p\), \[ C_4(p):=\sum_{m=0}^{p-1}\left|\sum_{n=0}^{p-1}\mathrm{e}\left(\frac{n^2(m+n)}{p}\right)\right|^4=2p^3+O(p^{5/2}), \] where \(\mathrm{e}(x)=e^{2\pi ix}\). They consider two cases when \(p-1\) is divisible by \(3\) or not.
Wang Xuexia, Wang Li
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.
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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
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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

New Identities Involving Certain Hardy Sums and Two-Term Exponential Sums

Indian Journal of Pure and Applied Mathematics, 2023
Muhammet Cihat Dagli
exaly  

The Fourth Power Mean of the Generalized Two-Term Exponential Sums and Its Upper and Lower Bound Estimates

Journal of Inequalities and Applications, 2013
Zhefeng Xu, Xiaoxue Li
exaly  

Bounds for Triple Exponential Sums With Mixed Exponential and Linear Terms

Bulletin of the Australian Mathematical Society, 2018
Kam Hung Yau
exaly  

The Mean Value Involving Dedekind Sums and Two-Term Exponential Sums

Science China Mathematics, 2012
exaly