[Fractions continues palindromes]
Dans cet article, nous considérons des nombres réels dont la suite des quotients partiels jouit de certaines propriétés de symétrie faisant intervenir la notion de palindrome. Nous obtenons trois nouveaux critères de transcendance s’appliquant à une grande classe de fractions continues, qu’elles soient à quotients partiels bornés ou non. Les démonstrations de ces résultats reposent sur le théorème du sous-espace de Schmidt.
In the present work, we investigate real numbers whose sequence of partial quotients enjoys some combinatorial properties involving the notion of palindrome. We provide three new transendence criteria, that apply to a broad class of continued fraction expansions, including expansions with unbounded partial quotients. Their proofs heavily depend on the Schmidt Subspace Theorem.
Keywords: Continued fractions, palindromes, transcendental numbers, Subspace Theorem.
Mot clés : Fractions continues, palindromes, nombres transcendants, théorème du sous-espace.
@article{AIF_2007__57_5_1557_0,
author = {Adamczewski, Boris and Bugeaud, Yann},
title = {Palindromic continued fractions},
journal = {Annales de l'Institut Fourier},
pages = {1557--1574},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {57},
number = {5},
year = {2007},
doi = {10.5802/aif.2306},
zbl = {1126.11036},
mrnumber = {2364142},
language = {en},
url = {http://www.numdam.org/articles/10.5802/aif.2306/}
}
TY - JOUR AU - Adamczewski, Boris AU - Bugeaud, Yann TI - Palindromic continued fractions JO - Annales de l'Institut Fourier PY - 2007 SP - 1557 EP - 1574 VL - 57 IS - 5 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2306/ DO - 10.5802/aif.2306 LA - en ID - AIF_2007__57_5_1557_0 ER -
%0 Journal Article %A Adamczewski, Boris %A Bugeaud, Yann %T Palindromic continued fractions %J Annales de l'Institut Fourier %D 2007 %P 1557-1574 %V 57 %N 5 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2306/ %R 10.5802/aif.2306 %G en %F AIF_2007__57_5_1557_0
Adamczewski, Boris; Bugeaud, Yann. Palindromic continued fractions. Annales de l'Institut Fourier, Tome 57 (2007) no. 5, pp. 1557-1574. doi : 10.5802/aif.2306. http://www.numdam.org/articles/10.5802/aif.2306/
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