A note on sequences not having metric Poissonian pair correlations
Number Theory
2021-01-12 v3
Abstract
The purpose of this note is to present a construction of sequences which do not have metric Poissonian pair correlations (MPPC) and whose additive energies grow at rates that come arbitrarily close to a threshold below which it is believed that all sequences have MPPC. A similar result appears in work of Lachmann and Technau and is proved using a totally different strategy. The main novelty here is the simplicity of the proof, which we arrive at by modifying a construction of Bourgain.
Cite
@article{arxiv.2008.02343,
title = {A note on sequences not having metric Poissonian pair correlations},
author = {Felipe A. Ramirez},
journal= {arXiv preprint arXiv:2008.02343},
year = {2021}
}
Comments
6 pages. v2: small changes in the exposition. Title has been re-worded