Van der Corput sets in Z^d
Dynamical Systems
2007-10-26 v1 Number Theory
Abstract
In this partly expository paper we study van der Corput sets in , with a focus on connections with harmonic analysis and recurrence properties of measure preserving dynamical systems. We prove multidimensional versions of some classical results obtained for in \cite{K-MF} and \cite{R}, establish new characterizations, introduce and discuss some modifications of van der Corput sets which correspond to various notions of recurrence, provide numerous examples and formulate some natural open questions.
Cite
@article{arxiv.0710.4861,
title = {Van der Corput sets in Z^d},
author = {Vitaly Bergelson and Emmanuel Lesigne},
journal= {arXiv preprint arXiv:0710.4861},
year = {2007}
}