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Mahler's method in several variables
Post-edited
Authors : Adamczewski, Boris (Author of the conference)
CIRM (Publisher )
11B85 - Automata sequences
11J81 - Transcendence (general theory)
11J85 - Algebraic independence; Gel'fond's method
CIRM (Publisher )
Abstract :
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.
MSC Codes : 11B85 - Automata sequences
11J81 - Transcendence (general theory)
11J85 - Algebraic independence; Gel'fond's method
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 18/09/2018 Conference Date : 12/09/2018 Subseries : Research talks arXiv category : Number Theory ; Combinatorics Mathematical Area(s) : Combinatorics ; Number Theory Format : MP4 (.mp4) - HD Video Time : 00:38:47 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2018-09-12_Adamczewski.mp4 
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Information on the Event
Event Title : Diophantine approximation and transcendence / Approximation diophantienne et transcendanceEvent Organizers : Adamczewski, Boris ; Bugeaud, Yann ; Habegger, Philipp ; Laurent, Michel ; Zannier, Umberto Dates : 10/09/2018 - 14/09/2018 Event Year : 2018 Event URL : https://conferences.cirm-math.fr/1841.html
Citation Data
DOI : 10.24350/CIRM.V.19445203Cite 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 |
See Also
- [Multi angle] Regulators of elliptic curves / Author of the conference Pazuki, Fabien.
- [Multi angle] Height pairings, torsion points, and dynamics / Author of the conference Krieger, Holly.
- [Multi angle] An effective criterion for periodicity of $p$-adic continued fractions / Author of the conference Capuano, Laura.
- [Multi angle] Simultaneous rational approximations to several functions of a real variable / Author of the conference Beresnevich, Victor.
Bibliography
- 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.
