## 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 language | English |
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Pages (from-to) | 249-256 |

Number of pages | 8 |

Journal | Bulletin of the London Mathematical Society |

Volume | 45 |

DOIs | |

Publication status | Published - Apr 2013 |

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