Additive energy and irregularities of distribution

Christoph Aistleitner, Gerhard Larcher

Research output: Contribution to journalArticlepeer-review


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
Original languageEnglish
Pages (from-to)99-107
JournalUniform Distribution Theory
Issue number1
Publication statusPublished - 2017


Dive into the research topics of 'Additive energy and irregularities of distribution'. Together they form a unique fingerprint.

Cite this