{
  "id": "2301.10359",
  "version": "v1",
  "published": "2023-01-25T00:13:14.000Z",
  "updated": "2023-01-25T00:13:14.000Z",
  "title": "Hecke Operators and Binary Quadratic Forms",
  "authors": [
    "Erik Bahnson",
    "Mark McConnell",
    "Kyrie McIntosh"
  ],
  "comment": "35 pages, 5 figures",
  "categories": [
    "math.NT"
  ],
  "abstract": "A new algorithm for computing Hecke operators for SL(n,Z) was introduced by MacPherson, McConnell in 2020. The algorithm uses tempered perfect lattices, which are certain pairs of lattices together with a quadratic form. These generalize the perfect lattices of Voronoi. The present paper is the first step in characterizing tempered perfect lattices. We obtain a complete classification in the plane, where the Hecke operators are for SL(2,Z) and its arithmetic subgroups. The results depend on the class field theory of orders in imaginary quadratic number fields.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-01-25T00:13:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F75",
      "11E16",
      "11F25",
      "11H55",
      "11R29"
    ],
    "keywords": [
      "binary quadratic forms",
      "tempered perfect lattices",
      "imaginary quadratic number fields",
      "class field theory",
      "computing hecke operators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}