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Approximations diophantiennes des nombres sturmiens

Martine Queffélec (2002)

Journal de théorie des nombres de Bordeaux

Nous établissons pour tout nombre sturmien (de développement dyadique sturmien) des propriétés d'approximation diophantienne très précises, ne dépendant que de l'angle de la suite sturmienne, généralisant ainsi des travaux antérieurs de Ferenczi-Mauduit et Bullett-Sentenac.

Arithmetic diophantine approximation for continued fractions-like maps on the interval

Avraham Bourla (2014)

Acta Arithmetica

We establish arithmetical properties and provide essential bounds for bi-sequences of approximation coefficients associated with the natural extension of maps, leading to continued fraction-like expansions. These maps are realized as the fractional part of Möbius transformations which carry the end points of the unit interval to zero and infinity, extending the classical regular and backwards continued fraction expansions.

Arithmetic Gevrey series and transcendence. A survey

Yves André (2003)

Journal de théorie des nombres de Bordeaux

We review the main results of the theory of arithmetic Gevrey series introduced in [3] [4], their applications to transcendence, and a few diophantine conjectures on the summation of divergent series.

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