{
  "id": "2106.12267",
  "version": "v1",
  "published": "2021-06-23T09:43:19.000Z",
  "updated": "2021-06-23T09:43:19.000Z",
  "title": "Rankin-Selberg integrals for ${\\rm SO}_{2n+1}\\times{\\rm GL}_r$ attached to New- and Oldforms",
  "authors": [
    "Yao Cheng"
  ],
  "comment": "30 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $\\pi$ and $\\tau$ be a smooth generic representation of ${\\rm SO}_{2n+1}$ and ${\\rm GL}_r$ over a non-archimedean field respectively. Suppose that $\\pi$ is irreducible and $\\tau$ has finite length that admits a unique Whittaker model. We consider the Rankin-Selberg integrals attached to (conjecutral) new- and oldforms in $\\pi$ in this paper. We show that such integrals always vanish if $\\tau$ is ramified and compute the integrals when $\\tau$ is unramified.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-23T09:43:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "rankin-selberg integrals",
      "smooth generic representation",
      "unique whittaker model",
      "finite length",
      "non-archimedean field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}