Afficher la notice abrégée

Algebraic solutions of linear differential equations: an arithmetic approach

hal.structure.identifierCalcul formel, mathématiques expérimentales et interactions [MATHEXP]
dc.contributor.authorBOSTAN, Alin
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
hal.structure.identifierLithe and fast algorithmic number theory [LFANT]
hal.structure.identifierAnalyse cryptographique et arithmétique [CANARI]
dc.contributor.authorCARUSO, Xavier
hal.structure.identifierInstitut Camille Jordan [ICJ]
hal.structure.identifierCombinatoire, théorie des nombres [CTN]
dc.contributor.authorROQUES, Julien
dc.date.accessioned2024-04-04T02:34:34Z
dc.date.available2024-04-04T02:34:34Z
dc.date.created2023-04-11
dc.date.issued2023-04-11
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/190563
dc.description.abstractEnGiven a linear differential equation with coefficients in $\mathbb{Q}(x)$, an important question is to know whether its full space of solutions consists of algebraic functions, or at least if one of its specific solutions is algebraic.After presenting motivating examples coming from various branches of mathematics, we advertise in an elementary way a beautiful local-global arithmetic approach to these questions, initiated by Grothendieck in the late sixties.This approach has deep ramifications and leads to the still unsolved Grothendieck-Katz $p$-curvature conjecture.
dc.description.sponsorshipCorrespondance de Langlands p-adique : une approche constructive et algorithmique - ANR-18-CE40-0026
dc.description.sponsorshipDécider l'irrationalité et la transcendance - ANR-19-CE40-0018
dc.description.sponsorshipAlgorithmes Efficaces pour Guessing, Inégalités, Sommation - ANR-22-CE91-0007
dc.language.isoen
dc.title.enAlgebraic solutions of linear differential equations: an arithmetic approach
dc.typeDocument de travail - Pré-publication
dc.subject.halMathématiques [math]
dc.subject.halInformatique [cs]
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
hal.identifierhal-04065092
hal.version1
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-04065092v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.date=2023-04-11&rft.au=BOSTAN,%20Alin&CARUSO,%20Xavier&ROQUES,%20Julien&rft.genre=preprint


Fichier(s) constituant ce document

FichiersTailleFormatVue

Il n'y a pas de fichiers associés à ce document.

Ce document figure dans la(les) collection(s) suivante(s)

Afficher la notice abrégée