A polynomial Roth theorem on the real line

Polona Durcik, Shaoming Guo, Joris Roos

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

For a polynomial P of degree greater than one, we show the existence of patterns of the form (x,x+t,x+P(t)) with a gap estimate on t 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.
Original languageEnglish
Pages (from-to)6973-6993
Number of pages18
JournalTransactions of the American Mathematical Society
Volume371
Issue number10
Early online date16 Jan 2019
DOIs
Publication statusPublished - 15 May 2019

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