Palindromic continued fractions

Adamczewski, Boris; Bugeaud, Yann

Annales de l'Institut Fourier, Tome 57 (2007) no. 5, pp. 1557-1574.

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.

Classification : 11J81, 11J70, 68R15
Keywords: Continued fractions, palindromes, transcendental numbers, Subspace Theorem.
Mot clés : Fractions continues, palindromes, nombres transcendants, théorème du sous-espace.

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