{
  "id": "1706.10010",
  "version": "v1",
  "published": "2017-06-30T03:38:57.000Z",
  "updated": "2017-06-30T03:38:57.000Z",
  "title": "IP$^{*}$-sets in function field and mixing properties",
  "authors": [
    "Dibyendu De",
    "Pintu Debnath"
  ],
  "journal": "Topology and its Applications 228, (2017), 294 -302",
  "categories": [
    "math.DS"
  ],
  "abstract": "The ring of polynomial over a finite field $F_q[x]$ has received much attention, both from a combinatorial viewpoint as in regards to its action on measurable dynamical systems. In the case of $(\\mathbb{Z},+)$ we know that the ideal generated by any nonzero element is an IP$^*$-set. In the present article we first establish that the analogous result is true for $F_q[x]$. We further use this result to establish some mixing properties of the action of $(F_q[x],+)$. We shall also discuss on Khintchine's recurrence for the action of $(F_q[x]\\setminus\\{0\\},\\cdot)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-30T03:38:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54D35",
      "22A15",
      "05D10",
      "54D80"
    ],
    "keywords": [
      "mixing properties",
      "function field",
      "khintchines recurrence",
      "nonzero element",
      "finite field"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}