{
  "id": "1711.00411",
  "version": "v1",
  "published": "2017-11-01T15:59:25.000Z",
  "updated": "2017-11-01T15:59:25.000Z",
  "title": "Values of quadratic forms on quasicrystals and a related problem",
  "authors": [
    "Oliver Sargent"
  ],
  "comment": "18 pages",
  "categories": [
    "math.NT",
    "math.DS"
  ],
  "abstract": "In this paper we study the set of values of quadratic form at points of a cut and project set. We will establish conditions which ensure that the set of values is dense. Our methods involve homogeneous dynamics and we will prove a orbit closure classification type result in this setting. This result has additional applications. In particular, we use it to study the set of integral values of a system consisting of a quadratic form and several linear forms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-01T15:59:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quadratic form",
      "related problem",
      "orbit closure classification type result",
      "quasicrystals",
      "linear forms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}