Minimization of differential equations and algebraic values of $E$-functions - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2022

Minimization of differential equations and algebraic values of $E$-functions

Résumé

A power series being given as the solution of a linear differential equation with appropriate initial conditions, minimization consists in finding a non-trivial linear differential equation of minimal order having this power series as a solution. This problem exists in both homogeneous and inhomogeneous variants; it is distinct from, but related to, the classical problem of factorization of differential operators. Recently, minimization has found applications in Transcendental Number Theory, more specifically in the computation of non-zero algebraic points where Siegel's $E$-functions take algebraic values. We present algorithms for these questions and discuss implementation and experiments.
Fichier principal
Vignette du fichier
2209.01827.pdf (456.7 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03771150 , version 1 (07-09-2022)
hal-03771150 , version 2 (18-07-2023)

Identifiants

  • HAL Id : hal-03771150 , version 1

Citer

Alin Bostan, Tanguy Rivoal, Bruno Salvy. Minimization of differential equations and algebraic values of $E$-functions. 2022. ⟨hal-03771150v1⟩
154 Consultations
202 Téléchargements

Partager

Gmail Mastodon Facebook X LinkedIn More