Results 11 to 20 of about 58,365 (183)

Equivariant Gauss sum of finite quadratic forms [PDF]

Forum Mathematicum, 2017
Abstract The classical quadratic Gauss sum can be thought of as an exponential sum attached to a quadratic form on a cyclic group. We introduce an equivariant version of Gauss sum for arbitrary finite quadratic forms, which is an exponential sum twisted by the action of the orthogonal group.
Shouhei Ma
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An asymptotic expansion for the generalised quadratic Gauss sum revisited [PDF]

Journal of Classical Analysis, 2014
An asymptotic expansion for the generalised quadratic Gauss sum $$S_N(x,θ)=\sum_{j=1}^{N} \exp (πixj^2+2πijθ),$$ where $x$, $θ$ are real and $N$ is a positive integer, is obtained as $x\rightarrow 0$ and $N\rightarrow\infty$ such that $Nx$ is finite. The form of this expansion holds for all values of $Nx+θ$ and, in particular, in the neighbourhood of ...
R. B. Paris
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The generalized quadratic Gauss sums and its sixth power mean

AIMS Mathematics, 2021
<abstract><p>In this article, we using elementary methods, the number of the solutions of some congruence equations and the properties of the Legendre's symbol to study the computational problem of the sixth power mean of a certain generalized quadratic Gauss sums, and to give an exact calculating formula for it.</p></abstract>
Xingxing Lv, Wenpeng Zhang
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A new sum analogous to quadratic Gauss sums and its 2k th power mean [PDF]

Journal of Inequalities and Applications, 2014
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
DU Xian-cun, Xiaoxue Li
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Motivating the Gauss sum proof of the quadratic reciprocity

, 2022
We try to motivate the Gauss sum proof of the quadratic reciprocity.
Pierre-Yves Gaillard
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Powers of Gauss sums in quadratic fields [PDF]

Journal of Number Theory, 2021
18 pages; 2 ...
Koji Momihara
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An hybrid mean value of quadratic Gauss sums and a sum analogous to Kloosterman sums [PDF]

Journal of Inequalities and Applications, 2014
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xiaowei Pan, Han Zhang
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Construction of Equientangled Bases in Arbitrary Dimensions via Quadratic Gauss Sums and Graph States [PDF]

, 2010
Recently [Karimipour and Memarzadeh, Phys. Rev. A 73, 012329 (2006)] studied the problem of finding a family of orthonormal bases in a bipartite space each of dimension $D$ with the following properties: (i) The family continuously interpolates between ...
Gheorghiu, Vlad, Looi, Shiang Yong
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ON THE GENERAL QUADRATIC GAUSS SUMS WEIGHTED BY CHARACTER SUMS OVER A SHORT INTERVAL [PDF]

Bulletin of the Korean Mathematical Society, 2013
Abstract. By using the analytic methods, the mean value of the generalquadratic Gauss sums weighted by the first power mean of character sumsover a short interval is investigated. Several sharp asymptotic formulaeare obtained, which show that these sums enjoy good distributive prop-erties. Moreover, interesting connections among them are established. 1.
Tianping Zhang
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Generalized quadratic Gauss sums and their 2mth power mean

Open Mathematics
Abstract The main purpose of this article is to study the problem of calculating the 2mth power mean of the generalized quadratic Gauss sums, and using the analytic method and an interesting combinatorial identity to give a sharp asymptotic formula for the 2mth power mean. Thus, a new simple proof of this existing result [N.
Di Cui, Wenpeng Zhang
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