{
  "id": "math/0610959",
  "version": "v1",
  "published": "2006-10-31T06:07:52.000Z",
  "updated": "2006-10-31T06:07:52.000Z",
  "title": "Trace formulas and class number sums",
  "authors": [
    "Nathan Jones"
  ],
  "comment": "21 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We specialize the Eichler-Selberg trace formula to obtain trace formulas for the prime-to-level Hecke action on cusp forms for certain congruence groups of arbitrary level. As a consequence, we determine the asymptotic in the prime p of the number of (weighted) SL(2,Z)-conjugation orbits of 2 by 2 matrices of determinant p whose reductions modulo N lie in a given conjugacy class in GL(2,Z/NZ). This generalizes an 1885 result of Hurwitz.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-10-31T06:07:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R29",
      "11F32"
    ],
    "keywords": [
      "class number sums",
      "eichler-selberg trace formula",
      "prime-to-level hecke action",
      "conjugacy class",
      "congruence groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....10959J"
    }
  }
}