{
  "id": "1903.03458",
  "version": "v1",
  "published": "2019-03-08T16:07:14.000Z",
  "updated": "2019-03-08T16:07:14.000Z",
  "title": "Test vectors for Rankin-Selberg $L$-functions",
  "authors": [
    "Andrew R. Booker",
    "M. Krishnamurthy",
    "Min Lee"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1804.07721",
  "categories": [
    "math.NT",
    "math.RT"
  ],
  "abstract": "We study the local zeta integrals attached to a pair of generic representations $(\\pi,\\tau)$ of $GL_n\\times GL_m$, $n>m$, over a $p$-adic field. Through a process of unipotent averaging we produce a pair of corresponding Whittaker functions whose zeta integral is non-zero, and we express this integral in terms of the Langlands parameters of $\\pi$ and $\\tau$. In many cases, these Whittaker functions also serve as a test vector for the associated Rankin-Selberg (local) $L$-function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-08T16:07:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F70",
      "11F66"
    ],
    "keywords": [
      "test vector",
      "rankin-selberg",
      "local zeta integrals",
      "generic representations",
      "adic field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}