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Hilbert series and Hilbert depth of squarefree Veronese ideals
Journal of Algebra, 2011 In this paper, we obtain explicit formulas for the Hilbert series and Hilbert depth of squarefree Veronese ideals in a standard graded polynomial ring.
Yulan Wang
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On a random series in a hilbert space
Canadian Journal of Statistics, 1978AbstractLet (Sn) be partial sums of a non‐degenerate sequence of Identically and independently distributed random variables taking values in a separable Hilbert space. Then for 0 ≤ β ≤ 3/2, the series converges almost nowhere. For β > 3/2 this may not be true.
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On the computation of the Hilbert series
2005We present an algorithm to compute the Hilbert series of a homogeneous ideal in a polynomial ring. From an ideal I, generated by the principal monomials of a Grobner basis, we compute the Hilbert series \(Hilb_{k[x_1 ,...,x_n ]/I}\)(t)=T I (t)/(1−t) n . The polynomial T I is computed by recursively factoring out a monomial m of degree d at each step
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Hilbert Series of Positive Braids
Algebra Colloquium, 2011Deligne proved that the Hilbert series of all Artin monoids are rational functions. We give an algorithm to compute the Hilbert series of the braid monoids [Formula: see text]. We also show that the Hilbert series of the positive words in [Formula: see text] with a given prefix are rational functions.
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On the Hilbert Series of Koszul Algebras
Functional Analysis and Its Applications, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The Hilbert series of prime PI rings
Israel Journal of Mathematics, 2004Let \(A\) be an algebra generated over a field \(k\) by a finite dimensional vector space \(V\) with \(1\in V\). The Hilbert series of \(A\) with respect to \(V\) is defined as \(1+\sum_{n\geq 1}\dim(V^n/V^{n-1})t^n\). The main result of the paper under review is that if \(A\) is a finitely generated prime PI-algebra, then its Hilbert series is ...
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Poincaré Series and Hilbert Modular Forms
The Ramanujan Journal, 2003\textit{W. Duke}, \textit{J. B. Friedlander} und \textit{H. Iwaniec} hatten 1994 [Invent. Math. 115, No. 2, 219--239 (1994; Zbl 0812.11032)] die aus den mit dem Faktor \(q(k-1)!(4\pi n)^{1-k}\) normierten Fourier\-koeffizienten \(\psi_f(n)\) der Funktionen \(f\) einer Orthonormalbasis \(F\) des Raumes der Spitzenformen zur Untergruppe \(\Gamma_0(q ...
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2010
An affine algebra A of positive Krull dimension is always infinite-dimensional as a vector space (see Theorem 5.11). The goal of introducing the Hilbert series is nevertheless to measure the size in some way. The trick is to break up A into finite-dimensional pieces, given by the degrees.
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An affine algebra A of positive Krull dimension is always infinite-dimensional as a vector space (see Theorem 5.11). The goal of introducing the Hilbert series is nevertheless to measure the size in some way. The trick is to break up A into finite-dimensional pieces, given by the degrees.
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Restriction of Coherent Hilbert Eisenstein series
Mathematische Annalen, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Multivariate Hilbert Series of Lattice Cones
Journal of Lie Theory, 2017Summary: We consider the dimensions of irreducible representations whose highest weights lie on a given lattice cone. We present a simple closed form for the multivariate formal power series which generates these dimensions. This closed form is a direct generalization of a formula for the Hilbert series of an equivariant embedding of a homogeneous ...
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