English
Mahler's method in several variables
Post-edited
Auteurs : Adamczewski, Boris (Auteur de la Conférence)
CIRM (Editeur )
11B85 - Automata sequences
11J81 - Transcendence (general theory)
11J85 - Algebraic independence; Gel'fond's method
CIRM (Editeur )
Résumé :
Any algebraic (resp. linear) relation over the field of rational functions with algebraic coefficients between given analytic functions leads by specialization to algebraic (resp. linear) relations over the field of algebraic numbers between the values of these functions. Number theorists have long been interested in proving results going in the other direction. Though the converse result is known to be false in general, Mahler's method provides one of the few known instances where it essentially holds true. After the works of Nishioka, and more recently of Philippon, Faverjon and the speaker, the theory of Mahler functions in one variable is now rather well understood. In contrast, and despite the contributions of Mahler, Loxton and van der Poorten, Kubota, Masser, and Nishioka among others, the theory of Mahler functions in several variables remains much less developed. In this talk, I will discuss recent progresses concerning the case of regular singular systems, as well as possible applications of this theory. This is a joint work with Colin Faverjon.
Codes MSC : 11B85 - Automata sequences
11J81 - Transcendence (general theory)
11J85 - Algebraic independence; Gel'fond's method
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 18/09/2018 Date de captation : 12/09/2018 Sous collection : Research talks arXiv category : Number Theory ; Combinatorics Domaine : Combinatorics ; Number Theory Format : MP4 (.mp4) - HD Durée : 00:38:47 Audience : Researchers Download : https://videos.cirm-math.fr/2018-09-12_Adamczewski.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Diophantine approximation and transcendence / Approximation diophantienne et transcendanceOrganisateurs de la rencontre : Adamczewski, Boris ; Bugeaud, Yann ; Habegger, Philipp ; Laurent, Michel ; Zannier, Umberto Dates : 10/09/2018 - 14/09/2018 Année de la rencontre : 2018 URL Congrès : https://conferences.cirm-math.fr/1841.html
Données de citation
DOI : 10.24350/CIRM.V.19445203Citer cette vidéo: Adamczewski, Boris (2018). Mahler's method in several variables. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19445203 URI : http://dx.doi.org/10.24350/CIRM.V.19445203 |
Voir aussi
- [Multi angle] Regulators of elliptic curves / Auteur de la Conférence Pazuki, Fabien.
- [Multi angle] Height pairings, torsion points, and dynamics / Auteur de la Conférence Krieger, Holly.
- [Multi angle] An effective criterion for periodicity of $p$-adic continued fractions / Auteur de la Conférence Capuano, Laura.
- [Multi angle] Simultaneous rational approximations to several functions of a real variable / Auteur de la Conférence Beresnevich, Victor.
Bibliographie
- Adamczewski, B., & Faverjon, C. (2018). Mahler's method in several variables I: The theory of regular singular systems.
- Adamczewski, B., & Faverjon, C. (2018). Mahler's method in several variables II: Applications to base change problems and finite automata.
