On the fractional parts of an/n. (30th September 2012)

• Record Type: Journal Article
• Authors: Cilleruelo, Javier; Kumchev, Angel; Luca, Florian; Rué, Juanjo; Shparlinski, Igor E.
• Is Part Of: Bulletin of the London Mathematical Society. Volume 45:Part 2(2013:Apr.)
• Page Start: 249
• Page End: 256
• Publication Date: 2012-09-30
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1112/blms/bds084
• Languages: English
• ISSNs: 0024-6093

Abstract

Abstract : We give various results about the distribution of the sequence { a n / n } n ⩾ 1 modulo 1, where a ⩾ 2 is a fixed integer. In particular, we find an explicit infinite subsequence 풜 such that { a n / n } n ∈풜 is uniformly distributed modulo 1. Also we show that for any constant c > 0 and a sufficiently large N, the fractional parts of the first N terms of this sequence hit every interval 풥 ⊆ [0, 1] of length |풥| ⩾ c N −0.475 .