Meilleures approximations diophantiennes simultanées et théorème de Lévy  [ Best simultaneous Diophantine approximations and Lévy's theorem ]
Annales de l'Institut Fourier, Volume 55 (2005) no. 5, p. 1635-1657
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.
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.
DOI : https://doi.org/10.5802/aif.2134
Classification:  11J13,  11J70,  22F30
Keywords: Diophantine approximations, Lévy's theorem, lattices
@article{AIF_2005__55_5_1635_0,
     author = {Chevallier, Nicolas},
     title = {Meilleures approximations diophantiennes simultan\'ees et th\'eor\`eme de L\'evy},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {55},
     number = {5},
     year = {2005},
     pages = {1635-1657},
     doi = {10.5802/aif.2134},
     zbl = {1080.11052},
     mrnumber = {2172275},
     language = {fr},
     url = {http://www.numdam.org/item/AIF_2005__55_5_1635_0}
}
Chevallier, Nicolas. Meilleures approximations diophantiennes simultanées et théorème de Lévy. Annales de l'Institut Fourier, Volume 55 (2005) no. 5, pp. 1635-1657. doi : 10.5802/aif.2134. http://www.numdam.org/item/AIF_2005__55_5_1635_0/

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