{
  "id": "2110.09466",
  "version": "v2",
  "published": "2021-10-18T16:59:15.000Z",
  "updated": "2022-06-22T17:53:39.000Z",
  "title": "Geometry-of-numbers methods in the cusp",
  "authors": [
    "Arul Shankar",
    "Artane Siad",
    "Ashvin Swaminathan",
    "Ila Varma"
  ],
  "comment": "29 pages",
  "categories": [
    "math.NT",
    "math.RT"
  ],
  "abstract": "In this article, we develop new methods for counting integral orbits having bounded invariants that lie inside the cusps of fundamental domains for coregular representations. We illustrate these methods for a representation of cardinal interest in number theory, namely that of the split orthogonal group acting on the space of quadratic forms.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-06-22T17:53:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R29",
      "11R45",
      "11H55",
      "11P21",
      "11E76"
    ],
    "keywords": [
      "geometry-of-numbers methods",
      "cardinal interest",
      "fundamental domains",
      "coregular representations",
      "counting integral orbits"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}