On the complexity of algebraic numbers

• Autores: Boris Adamczewski, Yann Bugeaud
• Localización: Annals of mathematics, ISSN 0003-486X, Vol. 165, Nº 2, 2007, págs. 547-565
• Idioma: inglés
• DOI: 10.4007/annals.2007.165.547
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• Resumen

  • Let b . 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.