Automatic Continued Fractions Are Transcendental or Quadratic
نویسنده
چکیده
We establish new combinatorial transcendence criteria for continued fraction expansions. Let α = [0; a1, a2, . . .] be an algebraic number of degree at least three. One of our criteria implies that the sequence of partial quotients (a`)`≥1 of α is not ‘too simple’ (in a suitable sense) and cannot be generated by a finite automaton. Résumé. Nous établissons de nouveaux critères combinatoires de transcendance pour des développements en fraction continue. Soit α = [0; a1, a2, . . .] un nombre algébrique de degré au moins égal à trois. L’un de nos critères entrâıne que la suite (a`)`≥1 des quotients partiels de α n’est pas trop simple (en un certain sens) et ne peut pas être engendrée par un automate fini.
منابع مشابه
Continued fractions and transcendental numbers
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