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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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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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On the Hybrid Power Mean Involving the Character Sums and Dedekind Sums
Journal of Mathematics, 2021 The main purpose of this paper is to use the elementary and analytic methods, the properties of Gauss sums, and character sums to study the computational problem of a certain hybrid power mean involving the Dedekind sums and a character sum analogous to ...
Xiaoling Xu
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A Hybrid Power Mean Involving the Dedekind Sums and Cubic Gauss Sums
Journal of Mathematics, 2021 The main purpose of this paper is using analytic methods and the properties of the Dedekind sums to study one kind hybrid power mean calculating problem involving the Dedekind sums and cubic Gauss sum and give some interesting calculating formulae for it.
Jiayuan Hu, Yu Zhan, Qin Si
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A new iteration method for solving space fractional coupled nonlinear Schrödinger equations [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2022 A linearly implicit difference scheme for the space fractional coupled nonlinear Schrödinger equation is proposed. The resulting coefficient matrix of the discretized linear system consists of the sum of a complex scaled identity and a symmetric positive ...
H. Aslani +2 more
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The quantum-mechanical Coulomb propagator in an L2 function representation
Scientific Reports, 2021 The quantum-mechanical Coulomb propagator is represented in a square-integrable basis of Sturmian functions. Herein, the Stieltjes integral containing the Coulomb spectral function as a weight is evaluated.
Rolf Gersbacher, John T. Broad
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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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A Two-Filter Approach for State Estimation Utilizing Quantized Output Data
Sensors, 2021 Filtering and smoothing algorithms are key tools to develop decision-making strategies and parameter identification techniques in different areas of research, such as economics, financial data analysis, communications, and control systems.
Angel L. Cedeño +4 more
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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
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Gauss sums and quantum mechanics [PDF]
Journal of Physics A: Mathematical and General, 2000 By adapting Feynman's sum over paths method to a quantum mechanical system whose phase space is a torus, a new proof of the Landsberg-Schaar identity for quadratic Gauss sums is given. In contrast to existing non-elementary proofs, which use infinite sums and a limiting process or contour integration, only finite sums are involved.
Armitage, Vernon, Rogers, Alice
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