On the complexity of algebraic numbers; [Sur la complexité des nombres algébriques]

Let b≥2 be an integer. We prove that real numbers whose b-ary expansion satisfies some given, simple, combinatorial condition are transcendental. This implies that the b-ary expansion of any algebraic irrational number cannot be generated by a finite automaton. © 2004 Académie des sciences. Publié par Elsevier SAS. Tous droits réservés.