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The Generalized Quadratic Gauss Sum and Its Fourth Power Mean
Mathematics, 2019 In this article, our main purpose is to introduce a new and generalized quadratic Gauss sum. By using analytic methods, the properties of classical Gauss sums, and character sums, we consider the calculating problem of its fourth power mean and give two ...
Shimeng Shen, Wenpeng Zhang
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Dirichlet characters of the rational polynomials
AIMS Mathematics, 2022 Denote by $ \chi $ a Dirichlet character modulo $ q\geq 3 $, and $ \overline{a} $ means $ a\cdot\overline{a} \equiv 1 \bmod q $. In this paper, we study Dirichlet characters of the rational polynomials in the form $ \sum\limits^{q}_{a = 1}'\chi(ma ...
Wenjia Guo, Xiaoge Liu, Tianping Zhang
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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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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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A Kronecker-type identity and the representations of a number as a sum of three squares [PDF]
, 2017 By considering a limiting case of a Kronecker-type identity, we obtain an identity found by both Andrews and Crandall. We then use the Andrews-Crandall identity to give a new proof of a formula of Gauss for the representations of a number as a sum of ...
Mortenson, E.
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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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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 recurrence formula for the number of solutions of a equation in finite field
AIMS Mathematics, 2021 The main purpose of this paper is using analytic methods to give a recurrence formula of the number of solutions of an equation over finite field. We use analytic methods to give a recurrence formula for the number of solutions of the above equation. And
Yanbo Song
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Upper bound estimate of incomplete Cochrane sum
Open Mathematics, 2017 By using the properties of Kloosterman sum and Dirichlet character, an optimal upper bound estimate of incomplete Cochrane sum is given.
Ma Yuankui, Peng Wen, Zhang Tianping
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Identities on quadratic Gauss sums [PDF]
Transactions of the American Mathematical Society, 1990 Given a local field F F , each multiplicative character θ \theta of the split algebra F × F F \times F or of a separable quadratic extension of F F has an associated generalized Gauss sum γ θ F \gamma _\theta ^F .
Paul Gerardin, Wen-Ch' Ing Winnie Li
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