On the Maillet--Baker continued fractions

Boris Adamczewski (1) , Yann Bugeaud (2)

1 ICJ - Institut Camille Jordan
2 IRMA - Institut de Recherche Mathématique Avancée

We use the Schmidt Subspace Theorem to establish the transcendence of a class of quasi-periodic continued fractions. This improves earlier works of Maillet and of A. Baker. We also improve an old result of Davenport and Roth on the rate of increase of the denominators of the convergents to any real algebraic number.

Mots clés: Transcendental numbers; continued fractions; Subspace Theorem

Domaines: Théorie des nombres [math.NT]

Boris Adamczewski, Yann Bugeaud. On the Maillet--Baker continued fractions. 2005. ⟨hal-00014590⟩