A polynomial Roth theorem on the real line
Combinatorics
2019-07-02 v3 Classical Analysis and ODEs
Abstract
For a polynomial of degree greater than one, we show the existence of patterns of the form with a gap estimate on in positive density subsets of the reals. This is an extension of an earlier result of Bourgain. Our proof is a combination of Bourgain's approach and more recent methods that were originally developed for the study of the bilinear Hilbert transform along curves.
Cite
@article{arxiv.1704.01546,
title = {A polynomial Roth theorem on the real line},
author = {Polona Durcik and Shaoming Guo and Joris Roos},
journal= {arXiv preprint arXiv:1704.01546},
year = {2019}
}
Comments
18 pages, to appear in Transactions of the AMS