On the fractional parts of an/n. (30th September 2012) - Cilleruelo, Javier; Kumchev, Angel; Luca, Florian; Rué, Juanjo; Shparlinski, Igor E.
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 .