Diophantine approximation and transcendence / Approximation diophantienne et transcendance

Collection Diophantine approximation and transcendence / Approximation diophantienne et transcendance

Organisateur(s) Adamczewski, Boris ; Bugeaud, Yann ; Habegger, Philipp ; Laurent, Michel ; Zannier, Umberto

Date(s) 10/09/2018 - 14/09/2018

URL associée https://conferences.cirm-math.fr/1841.html

00:00:00 / 00:00:00

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An effective criterion for periodicity of $p$-adic continued fractions

De Laura Capuano

It goes back to Lagrange that a real quadratic irrational has always a periodic continued fraction. Starting from decades ago, several authors proposed different definitions of a $p$-adic continued fraction, and the definition depends on the chosen system of residues mod $p$. It turns out that the theory of p-adic continued fractions has many differences with respect to the real case; in particular, no analogue of Lagranges theorem holds, and the problem of deciding whether the continued fraction is periodic or not seemed to be not known until now. In recent work with F. Veneziano and U. Zannier we investigated the expansion of quadratic irrationals, for the $p$-adic continued fractions introduced by Ruban, giving an effective criterion to establish the possible periodicity of the expansion. This criterion, somewhat surprisingly, depends on the ‘real’ value of the $p$-adic continued fraction.

Informations sur la vidéo

Date de captation 11/09/2018
Date de publication 26/09/2018
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.19445503
Citer cette vidéo Capuano, Laura (11/09/2018). An effective criterion for periodicity of $p$-adic continued fractions. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19445503
URL https://dx.doi.org/10.24350/CIRM.V.19445503

Domaine(s)

Théorie des nombres

Bibliographie

Capuano, L., Veneziano, F., & Zannier, U. (2018). An effective criterion for periodicity of l-adic continued fractions. <arXiv:1801.06214> - https://arxiv.org/abs/1801.06214

Codes MSC

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