Geodesic
On the complexity of algebraic numbers I. Expansions in integer bases
Boris Adamczewski1 ; Yann Bugeaud2
1 Département Mathématiques, CNRS, Université Claude Bernard Lyon 1, 69622 Villeurbanne, France
2 L'UFR de Mathématique et d'Informatique, Université Louis Pasteur, 67084 Strasbourg, France
Annals of mathematics, Tome 165 (2007) no. 2, pp. 547-565.

Voir la notice de l'article provenant de la source Annals of Mathematics website

Let $b \ge 2$ be an integer. We prove that the $b$-ary 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.
DOI : 10.4007/annals.2007.165.547

Boris Adamczewski 1 ; Yann Bugeaud 2

1 Département Mathématiques, CNRS, Université Claude Bernard Lyon 1, 69622 Villeurbanne, France
2 L'UFR de Mathématique et d'Informatique, Université Louis Pasteur, 67084 Strasbourg, France 
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Boris Adamczewski; Yann Bugeaud. On the complexity of algebraic numbers I. Expansions in integer bases. Annals of mathematics, Tome 165 (2007) no. 2, pp. 547-565. doi : 10.4007/annals.2007.165.547. http://geodesic.mathdoc.fr/articles/10.4007/annals.2007.165.547/

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