Polynomial bounds for the oscillation  of solutions of Fuchsian systems

Gal Binyamini; Sergei Yakovenko

Displaying similar documents to “Polynomial bounds for the oscillation of solutions of Fuchsian systems”

An explicit formula for period determinant

Alexey A. Glutsyuk (2006)

Annales de l’institut Fourier

Similarity:

We consider a generic complex polynomial in two variables and a basis in the first homology group of a nonsingular level curve. We take an arbitrary tuple of homogeneous polynomial 1-forms of appropriate degrees so that their integrals over the basic cycles form a square matrix (of multivalued analytic functions of the level value). We give an explicit formula for the determinant of this matrix.

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,...

Moduli spaces for linear differential equations and the Painlevé equations

Marius van der Put, Masa-Hiko Saito (2009)

Annales de l’institut Fourier

Similarity:

A systematic construction of isomonodromic families of connections of rank two on the Riemann sphere is obtained by considering the analytic Riemann–Hilbert map $R H : ℳ \to ℛ$ , where $ℳ$ is a moduli space of connections and $ℛ$ , , is a moduli space for analytic data (, ordinary monodromy, Stokes matrices and links). The assumption that the fibres of $R H$ (, the isomonodromic families) have dimension one, leads to ten moduli spaces $ℳ$ . The induced Painlevé equations are computed explicitly. Except for the...

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

Arzu Boysal, Michèle Vergne (2012)

Annales de l’institut Fourier

Similarity:

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...

Effective equidistribution of S-integral points on symmetric varieties

Yves Benoist, Hee Oh (2012)

Annales de l’institut Fourier

Similarity:

Let $K$ be a global field of characteristic not 2. Let $Z = H ∖ G$ be a symmetric variety defined over $K$ and $S$ a finite set of places of $K$ . We obtain counting and equidistribution results for the S-integral points of $Z$ . Our results are effective when $K$ is a number field.