{
  "id": "1407.3515",
  "version": "v1",
  "published": "2014-07-14T00:10:55.000Z",
  "updated": "2014-07-14T00:10:55.000Z",
  "title": "Automorphic forms for triangle groups: Integrality properties",
  "authors": [
    "Hossein Movasati",
    "Khosro M. Shokri"
  ],
  "comment": "To appear in Journal of Number Theory",
  "categories": [
    "math.NT",
    "math.CV"
  ],
  "abstract": "We classify all primes appearing in the denominators of the Hauptmodul $J$ and modular forms for non-arithmetic triangle groups with a cusp. These primes have a congruence condition in terms of the order of the generators of the group. As a corollary we show that for the Hecke group of type $(2,m,\\infty)$, the prime $p$ does not appear in the denominator of $J$ if and only if $p\\equiv \\pm 1\\pmod m$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-14T00:10:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "integrality properties",
      "automorphic forms",
      "non-arithmetic triangle groups",
      "hecke group",
      "denominator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.3515M"
    }
  }
}