Continued fractions and transcendental numbers

Adamczewski, Boris; Bugeaud, Yann; Davison, Les

doi:10.5802/aif.2234

Continued fractions and transcendental numbers
[Fractions continues et nombres transcendants]

Adamczewski, Boris ¹ ; Bugeaud, Yann ² ; Davison, Les ³

¹ Université Claude Bernard Lyon 1 Institut Camille Jordan, CNRS Bât. Braconnier, 21 avenue Claude Bernard 69622 VILLEURBANNE Cedex (FRANCE)
² Université Louis Pasteur UFR de mathématiques 67084 STRASBOURG Cedex (FRANCE)
³ Laurentian University Department of Mathematics and Computer Science Sudbury, Ontario P3E 2C6 (CANADA)

Annales de l'Institut Fourier, Tome 56 (2006) no. 7, pp. 2093-2113.

Résumé
Abstract

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].

MR Zbl | 4 citations dans Numdam

DOI : 10.5802/aif.2234

Classification : 11J81, 11J70, 68R15
Keywords: Continued fractions, transcendental numbers, subspace theorem
Mot clés : fractions continues, nombres transcendants, théorème du sous-espace

Affiliations des auteurs :

Adamczewski, Boris ¹ ; Bugeaud, Yann ² ; Davison, Les ³

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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://www.numdam.org/articles/10.5802/aif.2234/

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