Results 1 to 10 of about 164,472 (335)
A note on two-term exponential sum and the reciprocal of the quartic Gauss sums [PDF]
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
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A certain new Gauss sum and its fourth power mean
AIMS Mathematics, 2020 The main purpose of this paper is using the elementary methods and the properties of the Legendre symbol to study the computational problem of the fourth power mean of a certain generalized quadratic Gauss sum, and give two exact calculating formulae for
Yan Zhao, Wenpeng Zhang, Xingxing Lv
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Proceedings of the American Mathematical Society, 2005 Let \(p\) be a prime number, \(\theta\) be a nonzero element of the finite field \(\mathbb F_p\) of multiplicative order \(t \geq 1\), and let \(\mathcal Z = \{z_1, z_2, \dots, z_T\}\) be a sequence of elements of \(\mathbb Z / t\mathbb Z\). Given two polynomials \(f(X), g(X) \in \mathbb F_p[X]\), an additive character \(\psi\) of \(\mathbb F_p\), and ...
Cohen, Stephen D. +4 more
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Gauss Sum Factorization with Cold Atoms [PDF]
Physical Review Letters, 2008 4 pages, 5 ...
Gilowski, M. +6 more
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Acta Arithmetica, 1997 For a multiplicative character \(\chi\) and a nontrivial additive character \(\lambda\) of the finite field with \(q\) elements (\(q\) is a power of an odd prime), the `Gauss' sums \(\sum\lambda(\text{tr }w)\) over \(w\in\text{SO}^-(2n,q)\) and \(\sum\chi(\text{det }w)\lambda(\text{tr} w)\) over \(w\in O^-(2n,q)\) are considered.
Dae San Kim
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On sums of Kloosterman and Gauss sums [PDF]
Transactions of the American Mathematical Society, 2019 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Igor E. Shparlinski
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, 2009 This paper has been withdrawn by the authors due to the fact that the conjecture has indeed already long been established.
Kaneko, Masanobu, Matsuo, Hironori
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The number of rational points on a class of hypersurfaces in quadratic extensions of finite fields
Electronic Research Archive, 2023 Let $ q $ be an even prime power and let $ \mathbb{F}_{q} $ be the finite field of $ q $ elements. Let $ f $ be a nonzero polynomial over $ \mathbb{F}_{q^2} $ of the form $ f = a_{1}x_{1}^{m_{1}}+\dots+a_{s}x_{s}^{m_{s}}+y_{1}y_{2}+\dots+y_{n-1}y_{n}+y_ ...
Qinlong Chen , Wei Cao
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Bilinear sums of Gauss sums [PDF]
Acta Arithmetica, 2022 Let \(p \geq 3\) be a prime number. Motivated by results on bilinear sums of Kloosterman sums and their generalisations, the author considers sums with Gauss sums \[ G(m, n)=\sum_{x=1}^{p} \mathbf{e}_{p}\left(m x+n x^{2}\right), \] where \(\mathbf{e}_{p}(z)=\exp (2 \pi i z / p)\).
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A New Gauss Sum and Its Recursion Properties
Journal of Mathematics, 2021 In this paper, we introduce a new Gauss sum, and then we use the elementary and analytic methods to study its various properties and prove several interesting three-order linear recursion formulae for it.
Li Chen
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