Dérangements et nombres de Genocchi

Déterminant de Hankel Construit sur des Polynômes Liés aux Nombres de Dérangements

Groupes de Galois et nombres automatiques

Nombres de Pisots, matrices primitives et bêta-conjugués

Pisot numbers, primitive matrices and beta-conjugates. We show that given a Pisot number β, for any integer n large enough, there is a nonnegative primitive square matrix whose order is equal to the degree of β, and the matrix admits β for eingenvalue. Let β = a1/β + a2/β + · · ·+ an/β + · · · be the β-expansion of β. For any Pisot number β, the sequence (an)n≥1 is ultimately periodic i.e., for...

Un peu de théorie des nombres et de calcul formel au service de l'arithmétique des ordinateurs

Nombres réels de complexité sous-linéaire : mesures d’irrationalité et de transcendance

By means of a quantitative version of the Schmidt Subspace Theorem, we obtain irrationality and trancendence measures for real numbers whose expansion in an integer base has a sublinear complexity. We further give several applications of our general results to Sturmian, automatic, and morphic numbers, and to lacunary series. In particular, we extend a theorem on Sturmian numbers established by ...