Premium
On the fractional parts of a n / n
Author(s) -
Cilleruelo Javier,
Kumchev Angel,
Luca Florian,
Rué Juanjo,
Shparlinski Igor E.
Publication year - 2013
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bds084
Subject(s) - mathematics , combinatorics , mathematical physics
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 such that { a n / n } n ∈ 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 ⊆ [0, 1] of length || ⩾ c N −0.475 .