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 language | English |
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Pages (from-to) | 6973-6993 |
Number of pages | 18 |
Journal | Transactions of the American Mathematical Society |
Volume | 371 |
Issue number | 10 |
Early online date | 16 Jan 2019 |
DOIs | |
Publication status | Published - 15 May 2019 |