{
  "id": "math/0612439",
  "version": "v4",
  "published": "2006-12-15T12:32:11.000Z",
  "updated": "2007-01-05T04:23:39.000Z",
  "title": "Sublattices of finite index",
  "authors": [
    "Chunlei Liu"
  ],
  "comment": "Revised on Jan. 5, 2007",
  "categories": [
    "math.NT"
  ],
  "abstract": "Assuming the Gowers Inverse conjecture and the M\\\"{o}bius conjecture for the finite parameter $s$, Green-Tao verified Dickson's conjecture for lattices which are ranges of linear maps of complexity at most $s$. In this paper, we reformulate Green-Tao's theorem on Dickson's conjecture, and prove that, if $L$ is the range of a linear map of complexity $s$, and $L_1$ is a sublattice of $L$ of finite index, then $L_1$ is the range of a linear map of complexity $s$.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2007-01-05T04:23:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11P32"
    ],
    "keywords": [
      "finite index",
      "linear map",
      "sublattice",
      "gowers inverse conjecture",
      "green-tao verified dicksons conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....12439L"
    }
  }
}