Palindromic continued fractions
Annales de l'Institut Fourier, Volume 57 (2007) no. 5, p. 1557-1574
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.
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.
DOI : https://doi.org/10.5802/aif.2306
Classification:  11J81,  11J70,  68R15
Keywords: Continued fractions, palindromes, transcendental numbers, Subspace Theorem.
@article{AIF_2007__57_5_1557_0,
     author = {Adamczewski, Boris and Bugeaud, Yann},
     title = {Palindromic continued fractions},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {57},
     number = {5},
     year = {2007},
     pages = {1557-1574},
     doi = {10.5802/aif.2306},
     zbl = {1126.11036},
     mrnumber = {2364142},
     language = {en},
     url = {https://aif.centre-mersenne.org/item/AIF_2007__57_5_1557_0}
}
Palindromic continued fractions. Annales de l'Institut Fourier, Volume 57 (2007) no. 5, pp. 1557-1574. doi : 10.5802/aif.2306. https://aif.centre-mersenne.org/item/AIF_2007__57_5_1557_0/

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