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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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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 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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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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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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Gauss Quadrature for Integrals and Sums
International Journal of Pure and Applied Mathematics Research, 2023 Gauss quadrature integral approximation is extended to include integrals with a measure consisting of a continuous as well as a discrete component. That is, we give an approximation for the integral of a function plus its sum over a discrete weighted set.
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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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One Kind New Hybrid Power Mean and Its Computational Formulae
Journal of Mathematics, 2022 The main purpose of this study is to use the elementary and analytic methods and the properties of the classical Gauss sums to study the calculation problems of one kind of hybrid power mean involving the quadratic character sums and the two-term ...
Li Wang, Xuexia Wang
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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
Paul Gerardin, Wen-Ch' Ing Winnie Li
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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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