On the fractional parts of an/n

Javier Cilleruelo*, Angel Kumchev, Florian Luca, Juanjo Rué, Igor E. Shparlinski

*Corresponding author for this work

Research output: Contribution to journalArticle

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 A such that {a n/n}n∈A 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 J ⊆ [0, 1] of length |J| ≥ c N-0.475.

Original languageEnglish
Pages (from-to)249-256
Number of pages8
JournalBulletin of the London Mathematical Society
Volume45
DOIs
Publication statusPublished - Apr 2013

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