Multiple recurrence and convergence along the primes

Trevor D. Wooley*, Tamar D. Ziegler

*Corresponding author for this work

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

16 Citations (Scopus)

Abstract

Let E subset of Z be a set of positive upper density. Suppose that P-1, P-2, ... , P-k is an element of Z[X] are polynomials having zero constant terms. We show that the set E boolean AND (E - p(1)(p - 1)) boolean AND ... (E - P-k(P - 1)) is non-empty for some prime number p. Furthermore, we prove convergence in L-2 of polynomial multiple averages along the primes.

Translated title of the contributionMultiple recurrence and convergence along the primes
Original languageEnglish
Pages (from-to)1705-1732
Number of pages28
JournalAmerican Journal of Mathematics
Volume134
Issue number6
DOIs
Publication statusPublished - Dec 2012

Bibliographical note

Publisher: The Johns Hopkins University Press

Keywords

  • DIFFERENCE SETS
  • ERGODIC AVERAGES
  • SEQUENCES
  • THEOREM
  • POLYNOMIALS
  • NILSEQUENCES
  • VARIABLES
  • NUMBERS

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