Une nouvelle démonstration du théorème d'André sur les E-fonctions au sens large

Abstract : We give a new proof of a theorem of André (2014) stating that every polynomial relation over Qbar between values of a family of E-functions in the broad sense (f_1,..., f_n) arises from a polynomial relation over Qbar(z) between the f_i(z). To this end, we prove a structure theorem on the G-operators in the broad sense : we begin by proving an analogue of Chudnovsky's theorem (1984) for the G-functions in the broad sense ; we then deduce from this that the minimal operator of a G-function in the broad sense is fuchsian. This makes possible to adapt to the case of the E-functions in the broad sense a proof of a theorem of Beukers (2006) , which is an analogue of André's theorem in the case of the E-functions in the narrow sense.
Document type :
Preprints, Working Papers, ...
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-02024884
Contributor : Gabriel Lepetit <>
Submitted on : Tuesday, February 19, 2019 - 2:02:04 PM
Last modification on : Sunday, February 24, 2019 - 1:05:22 AM

File

Goplarges.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-02024884, version 1

Collections

Citation

Gabriel Lepetit. Une nouvelle démonstration du théorème d'André sur les E-fonctions au sens large. 2019. ⟨hal-02024884⟩

Share

Metrics

Record views

46

Files downloads

25