Nil-Bohr Sets of Integers
Dynamical Systems
2012-09-27 v1
Abstract
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 in both 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.
Cite
@article{arxiv.0903.1642,
title = {Nil-Bohr Sets of Integers},
author = {Bernard Host and Bryna Kra},
journal= {arXiv preprint arXiv:0903.1642},
year = {2012}
}