2180 articles – 2572 references  [version française]
 HAL: hal-00014597, version 1
 arXiv: math.NT/0511682
 Continued fractions and transcendental numbers
 (2005-11-28)
 It is widely believed that the continued fraction expansion of every irrational algebraic number $\alpha$ either is eventually periodic (and we know that this is the case if and only if $\alpha$ is a quadratic irrational), or it contains arbitrarily large partial quotients. Apparently, this question was first considered by Khintchine. A preliminary step towards its resolution consists in providing explicit examples of transcendental continued fractions. The main purpose of the present work is to present new families of transcendental continued fractions with bounded partial quotients. Our results are derived thanks to new combinatorial transcendence criteria recently obtained by Adamczewski and Bugeaud.
 1: Institut Camille Jordan (ICJ) CNRS : UMR5208 – Université Claude Bernard - Lyon I – Ecole Centrale de Lyon – Institut National des Sciences Appliquées (INSA) - Lyon 2: Institut de Recherche Mathématique Avancée (IRMA) CNRS : UMR7501 – Université Louis Pasteur - Strasbourg I 3: Department of Mathematics and Computer Science [Laurentian Univ.] laurantian university
 Subject : Mathematics/Number Theory
 Keyword(s): Transcendental numbers – continued fractions – Subspace Theorem
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 hal-00014597, version 1 http://hal.archives-ouvertes.fr/hal-00014597 oai:hal.archives-ouvertes.fr:hal-00014597 From: Boris Adamczewski <> Submitted on: Monday, 28 November 2005 14:57:29 Updated on: Wednesday, 1 October 2008 15:02:36