New results on algebraic independence with Mahlerʼs method

Evgeniy Zorin

doi:10.1016/j.crma.2011.05.012

Number Theory

New results on algebraic independence with Mahlerʼs method

Presented by: the Editorial Board

Evgeniy Zorin ¹

¹ Institut de mathématiques de Jussieu, Université Paris 7, 75005 Paris, France

Comptes Rendus. Mathématique, Volume 349 (2011) no. 11-12, pp. 607-610.

Abstract
Résumé

We give some new results on algebraic independence in the frame of Mahlerʼs method, including algebraic independence of values at transcendental points. We also give some new measures of algebraic independence. In particular, our results furnish for $n ⩾ 1$ arbitrarily large new examples of families of members $(θ_{1}, \dots, θ_{n}) \in R^{n}$ normal in the sense of the definition formulated by G. Chudnovsky (1980) [2].

Nous donnons quelques nouveaux résultats dʼindépendance algébrique de valeurs de fonctions satisfaisant des équations fonctionnelles, incluant lʼindépendance algébrique en un point transcendant. Ces resultats sont obtenus avec la méthode de Mahler. En particulier, certains de nos résultats fournissent pour $n ⩾ 1$ arbitrairement grand des nouvelles familles de nombres $(θ_{1}, \dots, θ_{n}) \in R^{n}$ normaux au sens de la définition formulée par G. Chudnovsky (1980) [2].

Received: 2011-03-25
Accepted: 2011-05-18
Published online: 2011-06-01

DOI: 10.1016/j.crma.2011.05.012

Author's affiliations:

Evgeniy Zorin ¹

¹ Institut de mathématiques de Jussieu, Université Paris 7, 75005 Paris, France

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     title = {New results on algebraic independence with {Mahler's} method},
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Evgeniy Zorin. New results on algebraic independence with Mahlerʼs method. Comptes Rendus. Mathématique, Volume 349 (2011) no. 11-12, pp. 607-610. doi : 10.1016/j.crma.2011.05.012. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.05.012/

References
Cited by

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