{
  "id": "1001.4081",
  "version": "v2",
  "published": "2010-01-22T21:18:47.000Z",
  "updated": "2010-11-30T20:05:22.000Z",
  "title": "Multiple recurrence and convergence along the primes",
  "authors": [
    "Trevor D. Wooley",
    "Tamar D. Ziegler"
  ],
  "comment": "Some changes made in light of comments from the referees",
  "categories": [
    "math.DS",
    "math.NT"
  ],
  "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.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-11-30T20:05:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B30",
      "11A41",
      "28D05",
      "37A05"
    ],
    "keywords": [
      "multiple recurrence",
      "convergence",
      "zero constant terms",
      "polynomial multiple averages",
      "positive upper density"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1001.4081W"
    }
  }
}