Automatic continued fractions are transcendental or quadratic
Bugeaud, Yann
Original · EN
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.
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