Multiple recurrence and convergence along the primes

Trevor D. Wooley, Tamar D. Ziegler

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


Let E ⊂ ℤ be a set of positive upper density. Suppose that P1,P2,...,Pk ∈ ℤ[X] are polynomials having zero constant terms. We show that the set E ∩ (E -P1(p-1)) ∩ ··· ∩ (E - Pk(p-1)) is non-empty for some prime number p. Furthermore, we prove convergence in L2 of polynomial multiple averages along the primes.

Original languageAmerican English
Pages (from-to)1705-1732
Number of pages28
JournalAmerican Journal of Mathematics
Issue number6
StatePublished - Dec 2012
Externally publishedYes


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