## Abstract

We consider strictly increasing sequences (an)n≥1 of integers and

sequences of fractional parts ({anα})n≥1 where α ∈ R. We show that a small

additive energy of (an)n≥1 implies that for almost all α the sequence ({anα})n≥1

has large discrepancy. We prove a general result, provide various examples, and

show that the converse assertion is not necessarily true

sequences of fractional parts ({anα})n≥1 where α ∈ R. We show that a small

additive energy of (an)n≥1 implies that for almost all α the sequence ({anα})n≥1

has large discrepancy. We prove a general result, provide various examples, and

show that the converse assertion is not necessarily true

Original language | English |
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Pages (from-to) | 99-107 |

Journal | Uniform Distribution Theory |

Volume | 12 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2017 |