Continued fractions and transcendental numbers
[Fractions continues et nombres transcendants]
Annales de l'Institut Fourier, Tome 56 (2006) no. 7, pp. 2093-2113.

L’objet principal de ce travail est de donner de nouvelles familles de fractions continues transcendantes dont la suite des quotients partiels est bornée. Les démonstrations de nos résultats reposent sur les critères combinatoires de transcendance récemment obtenus par les deux premiers auteurs dans [3].

The main purpose of this work is to present new families of transcendental continued fractions with bounded partial quotients. Our results are derived thanks to combinatorial transcendence criteria recently obtained by the first two authors in [3].

DOI : https://doi.org/10.5802/aif.2234
Classification : 11J81,  11J70,  68R15
Mots clés : fractions continues, nombres transcendants, théorème du sous-espace
@article{AIF_2006__56_7_2093_0,
     author = {Adamczewski, Boris and Bugeaud, Yann and Davison, Les},
     title = {Continued fractions and transcendental numbers},
     journal = {Annales de l'Institut Fourier},
     pages = {2093--2113},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {56},
     number = {7},
     year = {2006},
     doi = {10.5802/aif.2234},
     mrnumber = {2290775},
     zbl = {1152.11034},
     language = {en},
     url = {http://archive.numdam.org/articles/10.5802/aif.2234/}
}
Adamczewski, Boris; Bugeaud, Yann; Davison, Les. Continued fractions and transcendental numbers. Annales de l'Institut Fourier, Tome 56 (2006) no. 7, pp. 2093-2113. doi : 10.5802/aif.2234. http://archive.numdam.org/articles/10.5802/aif.2234/

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