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Journal of Mathematics, 2021 The main purpose of this paper is using the analytic method and the properties of the classical Gauss sums to study the computational problem of one kind hybrid power mean involving the quartic Gauss sums and two-term exponential sums and give an ...
Lan Qi, Xingxing Lv
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Journal of Mathematics, 2021 In this paper, we use the analytic methods and the properties of the classical Gauss sums to study the properties of the error term of the fourth power mean of the generalized cubic Gauss sums and give two recurrence formulae for it.
Zhang Jin, Zhang Jiafan
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Some new hybrid power mean formulae of trigonometric sums
Advances in Difference Equations, 2020 We apply the analytic method and the properties of the classical Gauss sums to study the computational problem of a certain hybrid power mean of the trigonometric sums and to prove several new mean value formulae for them.
Li Chen, Zhuoyu Chen
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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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Evaluations of a Weighted Average of Gauss Sums
Journal of Mathematics, 2021 In this paper, we perform a further investigation for a weighted average of Gauss sums. By making use of some properties of the cotangent function and the Bernoulli polynomials, we explicitly evaluate the weighted average of Gauss sums in terms of the ...
Wen-Kai Shao, Yuan He
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A Hybrid Mean Value Involving Dedekind Sums and the Generalized Kloosterman Sums
Journal of Mathematics, 2021 In this paper, we use the mean value theorem of Dirichlet L-functions and the properties of Gauss sums and Dedekind sums to study the hybrid mean value problem involving Dedekind sums and the general Kloosterman sums and give an interesting identity for ...
Xiaowei Pan, Xiaoyan Guo
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Hypergeometric decomposition of symmetric K3 quartic pencils [PDF]
, 2020 We study the hypergeometric functions associated to five one-parameter deformations of Delsarte K3 quartic hypersurfaces in projective space. We compute all of their Picard--Fuchs differential equations; we count points using Gauss sums and rewrite this ...
Doran, Charles F. +5 more
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Factorizing Numbers with the Gauss Sum Technique: NMR Implementations [PDF]
, 2007 Several physics-based algorithms for factorizing large number were recently published. A notable recent one by Schleich et al. uses Gauss sums for distinguishing between factors and non-factors.
Dieter Suter +8 more
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The hybrid power mean of the quartic Gauss sums and the two-term exponential sums
Advances in Difference Equations, 2018 In this paper, we use the analytic method and the properties of classical Gauss sums to study the computational problems of one kind hybrid power mean of quartic Gauss sums and two-term exponential sums, and give an interesting fourth-order linear ...
Xiaoxue Li
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Proceedings of the American Mathematical Society, 1956 where p is an odd prime, has been proved in a variety of ways. In particular the proof in [3, p. 623 ] may be cited. We remark that Estermann [1 ] has recently given a simple proof of (1) that is valid for arbitrary odd p. In the present note we indicate a short proof of (1) that makes use of some familiar results from cyclotomy. Let E = e27riP and let
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