{
  "id": "2303.02544",
  "version": "v2",
  "published": "2023-03-05T01:30:57.000Z",
  "updated": "2024-11-11T22:41:22.000Z",
  "title": "$L$-functions for $\\mathrm{Sp}(2n)\\times\\mathrm{GL}(k)$ via non-unique models",
  "authors": [
    "Yubo Jin",
    "Pan Yan"
  ],
  "comment": "37 pages. The main result on integral representation is strengthened to Sp(2n)xGL(k) for all positive integers n and k such that n is even",
  "categories": [
    "math.NT",
    "math.RT"
  ],
  "abstract": "Let $n$ and $k$ be positive integers such that $n$ is even. We derive new global integrals for $\\mathrm{Sp}_{2n}\\times\\mathrm{GL}_k$ from the generalized doubling method of Cai, Friedberg, Ginzburg and Kaplan, following a strategy and extending a previous result of Ginzburg and Soudry on the case $n=k=2$. We show that these new integrals unfold to non-unique models on $\\mathrm{Sp}_{2n}$. Using the New Way method of Piatetski-Shapiro and Rallis, we show that these new global integrals represent the $L$-functions for $\\mathrm{Sp}_{2n}\\times\\mathrm{GL}_k$, generalizing a previous result of the second-named author on $\\mathrm{Sp}_{4}\\times\\mathrm{GL}_2$ and a previous work of Piatetski-Shapiro and Rallis on $\\mathrm{Sp}_{2n}\\times\\mathrm{GL}_1$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-11-11T22:41:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F70",
      "11F55",
      "22E50",
      "22E55"
    ],
    "keywords": [
      "non-unique models",
      "global integrals represent",
      "way method",
      "piatetski-shapiro",
      "integrals unfold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}