Paradan’s wall crossing formula for partition functions and Khovanski-Pukhlikov differential operator

Arzu Boysal; Michèle Vergne

Displaying similar documents to “Paradan’s wall crossing formula for partition functions and Khovanski-Pukhlikov differential operator”

Multiple Bernoulli series, an Euler-MacLaurin formula, and Wall crossings

Arzu Boysal, Michèle Vergne (2012)

Annales de l’institut Fourier

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We study multiple Bernoulli series associated to a sequence of vectors generating a lattice in a vector space. The associated multiple Bernoulli series is a periodic and locally polynomial function, and we give an explicit formula (called wall crossing formula) comparing the polynomial densities in two adjacent domains of polynomiality separated by a hyperplane. We also present a formula in the spirit of Euler-MacLaurin formula. Finally, we give a decomposition formula for the Bernoulli...

Billiard complexity in the hypercube

Nicolas Bedaride, Pascal Hubert (2007)

Annales de l’institut Fourier

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We consider the billiard map in the hypercube of $ℝ^{d}$ . We obtain a language by coding the billiard map by the faces of the hypercube. We investigate the complexity function of this language. We prove that $n^{3 d - 3}$ is the order of magnitude of the complexity.

The higher transvectants are redundant

Abdelmalek Abdesselam, Jaydeep Chipalkatti (2009)

Annales de l’institut Fourier

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Let $A, B$ denote generic binary forms, and let $𝔲_{r} = {(A, B)}_{r}$ denote their $r$ -th transvectant in the sense of classical invariant theory. In this paper we classify all the quadratic syzygies between the ${𝔲_{r}}$ . As a consequence, we show that each of the higher transvectants ${𝔲_{r} : r \geq 2}$ is redundant in the sense that it can be completely recovered from $𝔲_{0}$ and $𝔲_{1}$ . This result can be geometrically interpreted in terms of the incomplete Segre imbedding. The calculations rely upon the Cauchy exact sequence of $S L_{2}$ -representations,...

Fourier Transforms of Measures and Algebraic Relations on Their Supports

Thomas W. Körner (2009)

Annales de l’institut Fourier

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We investigate the relation between the rate of decrease of a Fourier transform and the possible algebraic relations on its support.

Ramification and moduli spaces of finite flat models

Naoki Imai (2011)

Annales de l’institut Fourier

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We determine the type of the zeta functions and the range of the dimensions of the moduli spaces of finite flat models of two-dimensional local Galois representations over finite fields. This gives a generalization of Raynaud’s theorem on the uniqueness of finite flat models in low ramifications.