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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… Click to show full abstract
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.
Keywords:
theorem real;
real line;
polynomial roth;
roth theorem
Journal Title: Transactions of the American Mathematical Society
Year Published: 2019
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Journal Title: Transactions of the American Mathematical Society
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!