Metrical Results on the Distribution of Fractional Parts of Powers of Real Numbers. Issue 2 (29th November 2018)

• Record Type: Journal Article
• Authors: Bugeaud, Yann; Liao, Lingmin; Rams, Michał
• Is Part Of: Proceedings of the Edinburgh Mathematical Society. Volume 62:Issue 2(2019)
• Page Start: 505
• Page End: 521
• Publication Date: 2018-11-29
• Subjects: fractional parts of powers, -- Diophantine approximation, -- Hausdorff dimension; Primary 11K36, -- Secondary 11J71, -- 28A80; Mathematics -- Periodicals; 510
• DOI: 10.1017/S0013091518000585
• Languages: English
• ISSNs: 0013-0915

Abstract

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 .