[Nouveaux résultats dʼindépendance algébrique par la méthode de Mahler]
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 arbitrairement grand des nouvelles familles de nombres normaux au sens de la définition formulée par G. Chudnovsky (1980) [2].
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 arbitrarily large new examples of families of members normal in the sense of the definition formulated by G. Chudnovsky (1980) [2].
Accepté le :
Publié le :
@article{CRMATH_2011__349_11-12_607_0,
author = {Zorin, Evgeniy},
title = {New results on algebraic independence with {Mahler's} method},
journal = {Comptes Rendus. Math\'ematique},
pages = {607--610},
publisher = {Elsevier},
volume = {349},
number = {11-12},
year = {2011},
doi = {10.1016/j.crma.2011.05.012},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2011.05.012/}
}
TY - JOUR AU - Zorin, Evgeniy TI - New results on algebraic independence with Mahlerʼs method JO - Comptes Rendus. Mathématique PY - 2011 SP - 607 EP - 610 VL - 349 IS - 11-12 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2011.05.012/ DO - 10.1016/j.crma.2011.05.012 LA - en ID - CRMATH_2011__349_11-12_607_0 ER -
%0 Journal Article %A Zorin, Evgeniy %T New results on algebraic independence with Mahlerʼs method %J Comptes Rendus. Mathématique %D 2011 %P 607-610 %V 349 %N 11-12 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2011.05.012/ %R 10.1016/j.crma.2011.05.012 %G en %F CRMATH_2011__349_11-12_607_0
Zorin, Evgeniy. New results on algebraic independence with Mahlerʼs method. Comptes Rendus. Mathématique, Tome 349 (2011) no. 11-12, pp. 607-610. doi : 10.1016/j.crma.2011.05.012. http://www.numdam.org/articles/10.1016/j.crma.2011.05.012/
[1] Transcendence measures for the values of generalized Mahler functions in arbitrary characteristic, Publ. Math. Debrecen, Volume 45 (1994), pp. 269-282
[2] G.V. Chudnovsky, Measures of irrationality, transcendence and algebraic independence. Recent progress, in: J. Armitage (Ed.), Journées Arithmétiques, 1980, Cambridge Univ. Press, 1982, pp. 11–82.
[3] On the algebraic independence of holomorphic solutions of certain functional equations and their values, Math. Ann., Volume 227 (1977), pp. 9-50
[4] (Nesterenko, Yu.; Philippon, Patrice, eds.), Introduction to Algebraic Independence Theory, vol. 1752, Springer, 2001
[5] Algebraic independence of certain power series of algebraic numbers, J. Number Theory, Volume 23 (1986), pp. 353-364
[6] Mahler Functions and Transcendence, Lecture Notes in Math., vol. 1631, Springer, 1996
[7] F. Pellarin, An introduction to Mahlerʼs method for transcendence and algebraic independence, preprint, 2010. Disponible at . | HAL
[8] Une approche méthodique pour la transcendance et lʼindépendance algébrique de valeurs de fonctions analytiques, J. Number Theory, Volume 64 (1997), pp. 291-338
[9] Indépendance algébrique et K-fonctions, J. Reine Angew. Math., Volume 497 (1998), pp. 1-15
[10] Algebraic independence of the values of generalized Mahler functions, Acta Arithmetica, Volume LXX.2 (1995)
[11] E. Zorin, Lemmes de zéros et relations fonctionnelles, thèse de doctorat de lʼUniversité Paris 6, 2010. Accessible at http://tel.archives-ouvertes.fr/tel-00558073/fr/.
[12] E. Zorin, Zero order estimates for analytic functions, preprint, . | arXiv
Cité par Sources :
