no. 5
Meilleures approximations diophantiennes simultanées et théorème de Lévy
Chevallier, Nicolas1
1 Université de Haute Alsace, 4 rue des frères Lumière, 68093 Mulhouse (France)
Annales de l'Institut Fourier, Tome 55 (2005) no. 5, pp. 1635-1657.

D'après le théorème de Lévy, les dénominateurs du développement en fraction continue d'un réel croissent presque sûrement à une vitesse au plus exponentielle. Nous étendons cette estimation aux meilleures approximations diophantiennes simultanées de formes linéaires.

According to Lévy's theorem, the denominators of the continued fraction expansion of a real number almost surely grow at most at the rate of a geometric series. We extend this estimate to best simultaneous Diophantine approximations to a set of linear forms.

DOI : 10.5802/aif.2134
Classification : 11J13, 11J70, 22F30
Mot clés : approximations diophantiennes, théorème de Lévy, réseaux
Keywords: Diophantine approximations, Lévy's theorem, lattices
Chevallier, Nicolas 1

1 Université de Haute Alsace, 4 rue des frères Lumière, 68093 Mulhouse (France) 
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Chevallier, Nicolas. Meilleures approximations diophantiennes simultanées et théorème de Lévy. Annales de l'Institut Fourier, Tome 55 (2005) no. 5, pp. 1635-1657. doi : 10.5802/aif.2134. http://archive.numdam.org/articles/10.5802/aif.2134/

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