{
  "id": "1407.3573",
  "version": "v2",
  "published": "2014-07-14T09:13:05.000Z",
  "updated": "2015-01-05T17:41:52.000Z",
  "title": "Spherical averages of Siegel transforms for higher rank diagonal actions and applications",
  "authors": [
    "Jayadev S. Athreya",
    "Anish Ghosh",
    "Jimmy Tseng"
  ],
  "comment": "New title. Added comments concerning number fields (see Section 5)",
  "categories": [
    "math.DS",
    "math.NT"
  ],
  "abstract": "We investigate the geometry of approximates in multiplicative Diophantine approximation. Our main tool is a new multiparameter averaging result for Siegel transforms on the space of unimodular lattices in ${\\mathbb R}^n$ which is of independent interest.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-14T09:13:05.000Z",
      "title": "Multiparameter spherical averages of Siegel transforms and applications",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-01-05T17:41:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A17",
      "11K60"
    ],
    "keywords": [
      "higher rank diagonal actions",
      "siegel transforms",
      "spherical averages",
      "applications",
      "multiplicative diophantine approximation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.3573A"
    }
  }
}