Nil-Bohr Sets of Integers

Bernard Host; Bryna Kra

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arXiv · 0903.1642

Nil-Bohr Sets of Integers

Bernard Host·Bryna Kra

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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.

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Bernard Host, Bryna Kra. 2009-03-09. Nil-Bohr Sets of Integers. https://arxiv.org/abs/0903.1642

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