{
  "id": "math/0601549",
  "version": "v1",
  "published": "2006-01-23T12:42:36.000Z",
  "updated": "2006-01-23T12:42:36.000Z",
  "title": "A converse theorem for $Γ_0(13)$",
  "authors": [
    "J. B. Conrey",
    "David W. Farmer",
    "B. E. Odgers",
    "N. C. Snaith"
  ],
  "comment": "10 pages, LaTeX",
  "categories": [
    "math.NT"
  ],
  "abstract": "We prove that a Dirichlet series with a functional equation and Euler product of a particular form can only arise from a holomorphic cusp form on the Hecke congruence group $\\Gamma_0(13)$. The proof does not assume a functional equation for the twists of the Dirichlet series. The main new ingredient is a generalization of the familiar Weil's lemma that played a prominent role in previous converse theorems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-01-23T12:42:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F66"
    ],
    "keywords": [
      "converse theorem",
      "dirichlet series",
      "functional equation",
      "familiar weils lemma",
      "holomorphic cusp form"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......1549C"
    }
  }
}