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Pré-Publication, Document De Travail Année : 2005

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

Boris Adamczewski

Résumé

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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hal-00014567 , version 1 (28-11-2005)

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Boris Adamczewski, Yann Bugeaud. On the complexity of algebraic number I. Expansions in integer bases.. 2005. ⟨hal-00014567⟩
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