Metrical results on the distribution of fractional parts of powers of real numbers

Yann Bugeaud (1) , Lingmin Liao (2) , Michal Rams (3)

1 IRMA - Institut de Recherche Mathématique Avancée
2 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
3 PAN - Institut of Mathematics - Polish Academy of Sciences

Denote by {·} the fractional part. We establish several new metrical results on the distribution properties of the sequence ({x n }) n≥1. Many of them are presented in a more general framework, in which the sequence of functions (x → x n) n≥1 is replaced by a sequence (fn) n≥1 , under some growth and regularity conditions on the functions fn.

Domaines: Théorie des nombres [math.NT]; Systèmes dynamiques [math.DS]

Yann Bugeaud, Lingmin Liao, Michal Rams. Metrical results on the distribution of fractional parts of powers of real numbers. 2017. ⟨hal-01614076v1⟩