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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 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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One Kind Special Gauss Sums and their Mean Square Values
Journal of Mathematics, 2021 In this paper, we introduce one kind special Gauss sums; then, using the elementary and analytic methods to study the mean value properties of these kind sums, we obtain several exact calculating formulae for them.
Jianhong Zhao, Jiejie Gao
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Exponential transform of quadratic functional and multiplicative ergodicity of a Gauss-Markov process [PDF]
, 2013 The Laplace transform of partial sums of the square of a non-centered Gauss-Markov process, conditioning on its starting point, is explicitly computed.
Breton, Alain Le +2 more
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NMR experiment factors numbers with Gauss sums [PDF]
, 2006 We factor the number 157573 using an NMR implementation of Gauss sums.Comment: 4 pages 5 ...
H. Davenport +15 more
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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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Open Mathematics, 2018 The main purpose of this paper is to study the computational problem of one kind hybrid power mean involving two-term exponential sums and quartic Gauss sums using the analytic method and the properties of the classical Gauss sums, and to prove some ...
Shen Shimeng
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Clausen's series 3F2(1) with integral parameter differences and transformations of the hypergeometric function 2F2(x) [PDF]
, 2012 We obtain summation formulas for the hypergeometric series 3 F 2(1) with at least one pair of numeratorial and denominatorial parameters differing by a negative integer.
Miller, A. R., Paris, Richard B.
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Gauss Sums and Binomial Coefficients
Journal of Number Theory, 2002 Let \(p= tn+r\) be a prime which splits in \(\mathbb{Q}(\sqrt{-t})\) where \(t\) has one of the following forms \[ \begin{aligned} t= k>3 &\;\text{ for a prime } k\equiv 3\pmod 4,\\ t= 4k &\;\text{ for a prime } k\equiv 1\pmod 4,\\ t= 8k &\;\text{ for an odd prime } k.
Lee, DH, Hahn, SG Hahn, Sang-Geun
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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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