Nil-bohr sets of integers

Bernard Host*, Bryna Kra

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


We study relations between subsets of integers that are large, where large can be interpreted in terms of size (such as a set of positive upper density or a set with bounded gaps) or in terms of additive structure (such as a Bohr set). Bohr sets are fundamentally abelian in nature and are linked to Fourier analysis. Recently it has become apparent that a higher order, non-abelian, Fourier analysis plays a role both in additive combinatorics and in ergodic theory. Here we introduce a higher-order version of Bohr sets and give various properties of these objects, generalizing results of Bergelson, Furstenberg, and Weiss.

Original languageEnglish (US)
Pages (from-to)113-142
Number of pages30
JournalErgodic Theory and Dynamical Systems
Issue number1
StatePublished - Feb 2011

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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