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

Arzu Boysal; Michèle Vergne

Displaying similar documents to “Multiple Bernoulli series, an Euler-MacLaurin formula, and Wall crossings”

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

Arzu Boysal, Michèle Vergne (2009)

Annales de l’institut Fourier

Similarity:

Let $P (s)$ be a family of rational polytopes parametrized by inequations. It is known that the volume of $P (s)$ is a locally polynomial function of the parameters. Similarly, the number of integral points in $P (s)$ is a locally quasi-polynomial function of the parameters. Paul-Émile Paradan proved a jump formula for this function, when crossing a wall. In this article, we give an algebraic proof of this formula. Furthermore, we give a residue formula for the jump, which enables us to compute it. ...

Polynomial bounds for the oscillation of solutions of Fuchsian systems

Gal Binyamini, Sergei Yakovenko (2009)

Annales de l’institut Fourier

Similarity:

We study the problem of placing effective upper bounds for the number of zeroes of solutions of Fuchsian systems on the Riemann sphere. The principal result is an explicit (non-uniform) upper bound, polynomially growing on the frontier of the class of Fuchsian systems of a given dimension $n$ having $m$ singular points. As a function of $n, m$ , this bound turns out to be double exponential in the precise sense explained in the paper. As a corollary, we obtain a solution of the so-called...

Puiseux series polynomial dynamics and iteration of complex cubic polynomials

Jan Kiwi (2006)

Annales de l’institut Fourier

Similarity:

We let $𝕃$ be the completion of the field of formal Puiseux series and study polynomials with coefficients in $𝕃$ as dynamical systems. We give a complete description of the dynamical and parameter space of cubic polynomials in $𝕃 [ζ]$ . We show that cubic polynomial dynamics over $𝕃$ and $ℂ$ are intimately related. More precisely, we establish that some elements of $𝕃$ naturally correspond to the Fourier series of analytic almost periodic functions (in the sense of Bohr) which parametrize (near infinity)...

The higher transvectants are redundant

Abdelmalek Abdesselam, Jaydeep Chipalkatti (2009)

Annales de l’institut Fourier

Similarity:

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,...

Billiard complexity in the hypercube

Nicolas Bedaride, Pascal Hubert (2007)

Annales de l’institut Fourier

Similarity:

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.