{
  "id": "1305.4717",
  "version": "v2",
  "published": "2013-05-21T05:27:19.000Z",
  "updated": "2013-11-04T03:45:20.000Z",
  "title": "Multiple recurrence and convergence results associated to $\\mathbb{F}_{p}^ω$-actions",
  "authors": [
    "Vitaly Bergelson",
    "Terence Tao",
    "Tamar Ziegler"
  ],
  "comment": "44 pages, no figures. Referee suggestions implemented",
  "categories": [
    "math.DS"
  ],
  "abstract": "Using an ergodic inverse theorem obtained in our previous paper, we obtain limit formulae for multiple ergodic averages associated with the action of $\\mathbb{F}_{p}^{\\omega}$. From this we deduce multiple Khintchine-type recurrence results analogous to those for $\\mathbb{Z}$-systems obtained by Bergelson, Host, and Kra, and also present some new counterexamples in this setting.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-11-04T03:45:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A15",
      "37A30"
    ],
    "keywords": [
      "convergence results",
      "multiple recurrence",
      "deduce multiple khintchine-type recurrence results",
      "ergodic inverse theorem",
      "multiple khintchine-type recurrence results analogous"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 44,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1305.4717B"
    }
  }
}