{
  "id": "1912.01405",
  "version": "v1",
  "published": "2019-12-03T14:29:36.000Z",
  "updated": "2019-12-03T14:29:36.000Z",
  "title": "On triple product L-functions",
  "authors": [
    "Jayce R. Getz"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $\\pi=\\pi_1 \\otimes \\pi_2 \\otimes \\pi_3$ be a unitary cuspidal automorphic representation of $\\mathrm{GL}_3^3(\\mathbb{A}_F)$ where $F$ is a number field. Assume that $\\pi$ is everywhere tempered. Under suitable local hypotheses, for a sufficiently large finite set of places $S$ of $F$ we prove that the triple product $L$-function $L^S(s,\\pi,\\otimes^3)$ admits a meromorphic continuation to $\\mathrm{Re}(s) >\\tfrac{3}{4}$. We also give some information about the possible poles.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-03T14:29:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F66",
      "11F70"
    ],
    "keywords": [
      "triple product l-functions",
      "unitary cuspidal automorphic representation",
      "sufficiently large finite set",
      "suitable local hypotheses",
      "meromorphic continuation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}