{
  "id": "1809.06586",
  "version": "v1",
  "published": "2018-09-18T08:30:00.000Z",
  "updated": "2018-09-18T08:30:00.000Z",
  "title": "Two converse theorems for Maass forms",
  "authors": [
    "Michael Neururer",
    "Thomas Oliver"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We first prove a new converse theorem for Dirichlet series of Maass type which does not assume an Euler product. The underlying idea is a geometric generalisation of Weil's classical argument. By studying the asymptotics of hypergeometric functions, we then show that the theorem remains valid if we allow twists to have arbitrary poles.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-18T08:30:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "converse theorem",
      "maass forms",
      "theorem remains valid",
      "dirichlet series",
      "geometric generalisation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}