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H 2 Mahler's method in several variables

Auteurs : Adamczewski, Boris (Auteur de la Conférence)
CIRM (Editeur )

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natural numbers - finite automata Cobham’s theorem real numbers - finite automata decimal expansion of classical constants independence of automatic real numbers Mahler functions Ku. Nishioka’s theorem Mahler method in several variables lifting theorem purity theorem

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

    Informations sur la Vidéo

    Langue : Anglais
    Date de publication : 18/09/2018
    Date de captation : 12/09/2018
    Collection : Research talks
    Format : MP4 (.mp4) - HD
    Durée : 00:38:47
    Domaine : Combinatorics ; Number Theory
    Audience : Chercheurs ; Doctorants , Post - Doctorants
    Download : https://videos.cirm-math.fr/2018-09-12_Adamczewski.mp4

Informations sur la rencontre

Nom de la rencontre : Diophantine approximation and transcendence / Approximation diophantienne et transcendance
Organisateurs 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

Citation Data

DOI : 10.24350/CIRM.V.19445203
Cite this video as: 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

Bibliographie

  • Adamczewski, B., & Faverjon, C. (2018). Mahler's method in several variables I: The theory of regular singular systems. - https://arxiv.org/abs/1809.04823

  • Adamczewski, B., & Faverjon, C. (2018). Mahler's method in several variables II: Applications to base change problems and finite automata. - https://arxiv.org/abs/1809.04826



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