Meilleures approximations diophantiennes simultanées et théorème de Lévy
Chevallier, Nicolas
Annales de l'Institut Fourier, Tome 55 (2005), p. 1635-1657 / Harvested from Numdam
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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.

Publié le : 2005-01-01
DOI : https://doi.org/10.5802/aif.2134
Classification:  11J13,  11J70,  22F30
Mots clés: approximations diophantiennes, théorème de Lévy, réseaux 
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     title = {Meilleures approximations diophantiennes simultan\'ees et th\'eor\`eme de L\'evy},
     journal = {Annales de l'Institut Fourier},
     volume = {55},
     year = {2005},
     pages = {1635-1657},
     doi = {10.5802/aif.2134},
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Chevallier, Nicolas. Meilleures approximations diophantiennes simultanées et théorème de Lévy. Annales de l'Institut Fourier, Tome 55 (2005) pp. 1635-1657. doi : 10.5802/aif.2134. http://gdmltest.u-ga.fr/item/AIF_2005__55_5_1635_0/

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