{
  "id": "1606.06923",
  "version": "v1",
  "published": "2016-06-22T12:18:46.000Z",
  "updated": "2016-06-22T12:18:46.000Z",
  "title": "Near Counterexamples to Weil's Converse Theorem",
  "authors": [
    "Raphael S. Steiner"
  ],
  "comment": "5 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We show that in Weil's converse theorem the functional equations of multiplicative twists for at least the first $\\sqrt{\\frac{p-24}{3}}$ moduli are needed in order to prove the modularity for $\\Gamma_0(p)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-22T12:18:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F66",
      "11F11"
    ],
    "keywords": [
      "weils converse theorem",
      "counterexamples",
      "functional equations",
      "multiplicative twists"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}