Quadratic approximation to automatic continued fractions
Journal de théorie des nombres de Bordeaux, Volume 27 (2015) no. 2, p. 463-482

We study the sets of values taken by the exponents of quadratic approximation w 2 and w 2 * evaluated at real numbers whose sequence of partial quotients is generated by a finite automaton. Among other results, we show that these sets contain every sufficiently large rational number and also some transcendental numbers.

Nous étudions les ensembles des valeurs prises par les exposants d’approximation quadratique w 2 et w 2 * évalués aux nombres réels dont la suite des quotients partiels est engendrée par un automate fini. Entre autres résultats, nous montrons que ces ensembles contiennent tout nombre rationnel suffisamment grand et également des nombres transcendants.

DOI : https://doi.org/10.5802/jtnb.910
Classification:  11J70,  11J82
Keywords: Continued fraction, approximation by quadratic numbers, automatic sequence.
@article{JTNB_2015__27_2_463_0,
     author = {Bugeaud, Yann},
     title = {Quadratic approximation to automatic continued fractions},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {27},
     number = {2},
     year = {2015},
     pages = {463-482},
     doi = {10.5802/jtnb.910},
     zbl = {06504489},
     mrnumber = {3393163},
     language = {en},
     url = {http://www.numdam.org/item/JTNB_2015__27_2_463_0}
}
Bugeaud, Yann. Quadratic approximation to automatic continued fractions. Journal de théorie des nombres de Bordeaux, Volume 27 (2015) no. 2, pp. 463-482. doi : 10.5802/jtnb.910. http://www.numdam.org/item/JTNB_2015__27_2_463_0/

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