Automatic continued fractions are transcendental or quadratic
Yann Bugeaud (2013)
Annales scientifiques de l'École Normale Supérieure
Similarity:
We establish new combinatorial transcendence criteria for continued fraction expansions. Let be an algebraic number of degree at least three. One of our criteria implies that the sequence of partial quotients of is not ‘too simple’ (in a suitable sense) and cannot be generated by a finite automaton.