Multiple recurrence and convergence along the primes

Trevor D. Wooley; Tamar D. Ziegler

Multiple recurrence and convergence along the primes

Dynamical Systems 2015-06-08 v2 Number Theory

Authors: Trevor D. Wooley , Tamar D. Ziegler

Abstract

Let $E\subset \mathbb Z$ be a set of positive upper density. Suppose that $P_1,P_2,..., P_k\in \mathbb Z[X]$ are polynomials having zero constant terms. We show that the set $E\cap (E-P_1(p-1))\cap ... \cap (E-P_k(p-1))$ is non-empty for some prime number $p$ . Furthermore, we prove convergence in $L^2$ of polynomial multiple averages along the primes.

Keywords

additive number theory prime number theory positive polynomials

Cite

@article{arxiv.1001.4081,
  title  = {Multiple recurrence and convergence along the primes},
  author = {Trevor D. Wooley and Tamar D. Ziegler},
  journal= {arXiv preprint arXiv:1001.4081},
  year   = {2015}
}

Comments

Some changes made in light of comments from the referees

Multiple recurrence and convergence along the primes

Abstract

Keywords

Cite

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