Metrical Results on the Distribution of Fractional Parts of Powers of Real Numbers. Issue 2 (29th November 2018) - Bugeaud, Yann; Liao, Lingmin; Rams, Michał
Abstract: We establish several new metrical results on the distribution properties of the sequence ( x n ) n ≥1, where · denotes the fractional part. 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 ( f n ) n ≥1, under some growth and regularity conditions on the functions f n .