Polynomial configurations in the primes

Thai Hoang Le, Julia Wolf

Research output: Contribution to journalArticle (Academic Journal)peer-review

4 Citations (Scopus)

Abstract

The Bergelson-Leibman theorem states that if P_1, ..., P_k are polynomials with integer coefficients, then any subset of the integers of positive upper density contains a polynomial configuration x+P_1(m), ..., x+P_k(m), where x,m are integers. Various generalizations of this theorem are known. Wooley and Ziegler showed that the variable m can in fact be taken to be a prime minus 1, and Tao and Ziegler showed that the Bergelson-Leibman theorem holds for subsets of the primes of positive relative upper density. Here we prove a hybrid of the latter two results, namely that the step m in the Tao-Ziegler theorem can be restricted to the set of primes minus 1.
Original languageEnglish
Pages (from-to)n/a
Number of pages22
JournalInternational Mathematics Research Notices
Volumen/a
Early online date16 Aug 2013
DOIs
Publication statusPublished - 2013

Keywords

  • math.NT
  • math.CO
  • 11B30

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