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.
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.
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.
A general hypergeometric construction of linear forms in (odd) zeta values is presented. The construction allows to recover the records of Rhin and Viola for the irrationality measures of and , as well as to explain Rivoal’s recent result on infiniteness of irrational numbers in the set of odd zeta values, and to prove that at least one of the four numbers , , , and is irrational.