{
  "id": "1902.00880",
  "version": "v1",
  "published": "2019-02-03T11:16:45.000Z",
  "updated": "2019-02-03T11:16:45.000Z",
  "title": "Doubling Constructions and Tensor Product $L$-Functions: coverings of the symplectic group",
  "authors": [
    "Eyal Kaplan"
  ],
  "categories": [
    "math.NT",
    "math.RT"
  ],
  "abstract": "In this work we develop an integral representation for the partial $L$-function of a pair $\\pi\\times\\tau$ of genuine irreducible cuspidal automorphic representations, $\\pi$ of the $m$-fold covering of Matsumoto of the symplectic group $Sp_{2n}$, and $\\tau$ of a certain covering group of $GL_k$, with arbitrary $m$, $n$ and $k$. Our construction is based on the recent extension by Cai, Friedberg, Ginzburg and the author, of the classical doubling method of Piatetski-Shapiro and Rallis, from rank-$1$ twists to arbitrary rank twists. We prove a basic global identity for the integral and compute the local integrals with unramified data. Possible applications include an analytic definition of local factors for representations of covering groups, and a Shimura type lift of representations from covering groups to general linear groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-03T11:16:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F70",
      "11F55",
      "11F66",
      "22E50",
      "22E55"
    ],
    "keywords": [
      "symplectic group",
      "tensor product",
      "doubling constructions",
      "covering group",
      "genuine irreducible cuspidal automorphic representations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}