English

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 Zd\Z^d, 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 d=1d=1 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.

Keywords

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}
}
R2 v1 2026-06-21T09:36:25.329Z