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Yann Bugeaud
Quadratic approximation to automatic continued fractions
Journal de théorie des nombres de Bordeaux, 27 no. 2 (2015), p. 463-482, doi: 10.5802/jtnb.910
Article PDF | Analyses MR 3393163
Class. Math.: 11J70, 11J82
Mots clés: Continued fraction, approximation by quadratic numbers, automatic sequence.

Résumé - Abstract

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.

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