{
  "id": "1905.04909",
  "version": "v1",
  "published": "2019-05-13T08:42:23.000Z",
  "updated": "2019-05-13T08:42:23.000Z",
  "title": "Converse theorems for automorphic distributions and Maass forms of level N",
  "authors": [
    "Tadashi Miyazaki",
    "Fumihiro Sato",
    "Kazunari Sugiyama",
    "Takahiko Ueno"
  ],
  "comment": "73 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We investigate the relations for $L$-functions satisfying certain functional equation, summationa formulas of Voronoi-Ferrar type and Maass forms of integral and half-integral weight. Summation formulas of Voronoi-Ferrar type can be viewed as an automorphic property of distribution vectors of non-unitary principal series representations of the double covering group of $SL(2)$. Our goal is converse theorems for automorphic distributions and Maass forms of level $N$ characterizing them by analytic properties of the associated $L$-functions. As an application of our converse theorems, we construct Maass forms from the two-variable zeta functions related to quadratic forms studied by Peter and the fourth author.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-13T08:42:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "converse theorems",
      "automorphic distributions",
      "voronoi-ferrar type",
      "non-unitary principal series representations",
      "construct maass forms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 73,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}