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

Boris Adamczewski·Yann Bugeaud
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Abstract

Let $b \ge 2$ be an integer. We prove that the $b$-adic expansion of every irrational algebraic number cannot have 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 transcendence criterion.

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Boris Adamczewski, Yann Bugeaud. 2005-11-28. On the complexity of algebraic number I. Expansions in integer bases. https://arxiv.org/abs/math/0511674

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