Certain transformations and summations for generalized hypergeometric series with integral parameter differences [PDF]
, 2011 Certain transformation and summation formulas for generalized hypergeometric series with integral parameter differences are ...
Miller, A. R., Paris, Richard B.
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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.
openaire +1 more source
Block circulant matrices with circulant blocks, weil sums and mutually unbiased bases, II. The prime power case [PDF]
, 2007 In our previous paper \cite{co1} we have shown that the theory of circulant matrices allows to recover the result that there exists $p+1$ Mutually Unbiased Bases in dimension $p$, $p$ being an arbitrary prime number.
Berndt B. C. +7 more
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Infinite Families of Potential Modular Data Related to Quadratic Categories [PDF]
Communications in Mathematical Physics, 2019 We present several infinite families of potential modular data motivated by examples of Drinfeld centers of quadratic categories. In each case, the input is a pair of involutive metric groups with Gauss sums differing by a sign, along with some ...
Pinhas Grossman, Masaki Izumi
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The Evolution of the Local Induction Approximation for a Regular Polygon *
ESAIM: Proceedings and Surveys, 2014 In this paper, we consider the so-called local induction approximation (LIA): $$ \Xt = \Xs\wedge\Xss, $$ X
de la Hoz Francisco, Vega Luis
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AN IDENTITY ON THE 2m-TH POWER MEAN VALUE OF THE GENERALIZED GAUSS SUMS [PDF]
, 2011 . In this paper, using analytic method and the properties oftheLegendre’ssymbol,weproveanexactcalculatingformulaonthe2m-thpowermeanvalueofthegeneralizedquadraticGausssumsform≥2.ThissolvesaconjectureofHeandZhang[On the 2k-th power mean valueof the ...
Feng-Jung Liu, Quan-Hui Yang
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Higher Gauss sums of modular categories [PDF]
, 2019 The definitions of the $n^{th}$ Gauss sum and the associated $n^{th}$ central charge are introduced for premodular categories $\mathcal{C}$ and $n\in\mathbb{Z}$. We first derive an expression of the $n^{th}$ Gauss sum of a modular category $\mathcal{C}$,
Ng, Siu-Hung +2 more
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Lattices with many Borcherds products [PDF]
, 2015 We prove that there are only finitely many isometry classes of even lattices $L$ of signature $(2,n)$ for which the space of cusp forms of weight $1+n/2$ for the Weil representation of the discriminant group of $L$ is trivial.
Bruinier, Jan Hendrik +2 more
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Some special finite sums related to the three-term polynomial relations and their applications
Advances in Differential Equations, 2014 We define some finite sums which are associated with the Dedekind type sums and Hardy-Berndt type sums. The aim of this paper is to prove a reciprocity law for one of these sums. Therefore, we define a new function which is related to partial derivatives
Elif Çeti̇n, Y. Simsek, I. N. Cangul
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Complete Solving for Explicit Evaluation of Gauss Sums in the Index 2 Case
, 2010 Let $p$ be a prime number, $q=p^f$ for some positive integer $f$, $N$ be a positive integer such that $\gcd(N,p)=1$, and let $\k$ be a primitive multiplicative character of order $N$ over finite field $\fq$.
B. C. Berndt +18 more
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