Abstract:
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 (al) l≥1 of α cannot be generated by a
finite automaton, and that the complexity function of (al) l≥1 cannot
increase too slowly.