Results 11 to 20 of about 324,501 (284)
The Mean Values of Character Sums and Their Applications
Mathematics, 2021 In this paper, we use the elementary methods and properties of classical Gauss sums to study the calculation problems of some mean values of character sums of special polynomials, and obtained several interesting calculation formulae for them.
Jiafan Zhang, Yuanyuan Meng
doaj +3 more sources
On the two-term exponential sums and character sums of polynomials
Open Mathematics, 2019 The main aim of this paper is to use the analytic methods and the properties of the classical Gauss sums to research the computational problem of one kind hybrid power mean containing the character sums of polynomials and two-term exponential sums modulo
Ma Yuankui, Zhang Wenpeng
doaj +2 more sources
On the fourth-order linear recurrence formula related to classical Gauss sums
Open Mathematics, 2017 Let p be an odd prime with p ≡ 1 mod 4, k be any positive integer, ψ be any fourth-order character mod p. In this paper, we use the analytic method and the properties of character sums mod p to study the computational problem of G(k, p) = τk(ψ)+τk(ψ ...
Zhuoyu Chen, Wenpeng Zhang
doaj +2 more sources
Journal of MathematicsThe primary contribution of this paper is to research one kind special Kloosterman sums using analytic method. We translate one kind fourth power mean of the Kloosterman sums into the character sums of one kind polynomials. It is possible to construct an
Shushu Ning, Xuexia Wang
doaj +2 more sources
Pacific Journal of Mathematics, 1986 Let \(N\) be a multiplicative character on the finite field \(GF(q)\), where \(q\) is a power of an odd prime \(p\). For \(x\in GF(q)\), \(Tr(x)\) denotes the trace of \(x\) from \(GF(q)\) to \(GF(p)\), and \(\zeta^ x\) denotes \(\exp(2\pi i Tr(x)/p)\). Define \(\bar N\) by \(N\bar N=1\).
openaire +2 more sources
A note on two-term exponential sum and the reciprocal of the quartic Gauss sums
Advances in Difference Equations, 2021 The 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 ...
Wenpeng Zhang, Xingxing Lv
doaj +1 more source
A Hybrid Mean Value Involving the Two-Term Exponential Sums and Two-Term Character Sums
Journal of Applied Mathematics, 2014 The main purpose of this paper is using the properties of Gauss sums and the estimate for character sums to study the hybrid mean value problem involving the two-term exponential sums and two-term character sums and give an interesting asymptotic formula
Liu Miaohua, Li Xiaoxue
doaj +1 more source
A Bound for a Sum of Products of Two Characters and Its Application
Mathematics, 2023 Using the exponent pair method, a bound is derived for the sum ∑manb≤xχ1a(m)χ2b(n), where a,b are fixed positive integers, χ1,χ2 are primitive Dirichlet characters modulo q1 and q2, respectively, and χ1a,χ2b are not principal characters.
Teerapat Srichan
doaj +1 more source
On the High-Power Mean of the Generalized Gauss Sums and Kloosterman Sums
Mathematics, 2019 The main aim of this paper is to use the properties of the trigonometric sums and character sums, and the number of the solutions of several symmetry congruence equations to research the computational problem of a certain sixth power mean of the ...
Xinyu Liu, Wenpeng Zhang
doaj +1 more source
The existence of $\protect \mathbb{F}_q$-primitive points on curves using freeness
Comptes Rendus. Mathématique, 2022 Let $\mathcal{C}_Q$ be the cyclic group of order $Q$, $n$ a divisor of $Q$ and $r$ a divisor of $Q/n$. We introduce the set of $(r,n)$-free elements of $\mathcal{C}_Q$ and derive a lower bound for the number of elements $\theta \in \mathbb{F}_q$ for ...
Cohen, Stephen D. +2 more
doaj +1 more source