Adamczewski Boris & Yann Bugeaud

On the complexity of algebraic numbers I. Expansions in integer bases

Let $b\geq 2$ be an integer. We prove that the $b$-adic expansion of any irrational number cannot have a low complexity. Furthermore, we establish that irrational morphic numbers are transcendental, for a wide class of morphisms. In particular, irrational automatic numbers are transcendental. Our main tool is a new, combinatorial transcendance criterion.