{
  "id": "2303.16114",
  "version": "v1",
  "published": "2023-03-28T16:31:52.000Z",
  "updated": "2023-03-28T16:31:52.000Z",
  "title": "Algebraicity of $L$-values for $\\text{GSp}_4 \\times \\text{GL}_2$ and $\\text{GSp}_4 \\times \\text{GL}_2 \\times \\text{GL}_2$",
  "authors": [
    "David Loeffler",
    "Óscar Rivero"
  ],
  "comment": "16 pages, comments welcome",
  "categories": [
    "math.NT"
  ],
  "abstract": "We prove algebraicity results for critical $L$-values attached to the group $\\text{GSp}_4 \\times \\text{GL}_2$, and for Gan--Gross--Prasad periods which are conjecturally related to central $L$-values for $\\text{GSp}_4 \\times \\text{GL}_2 \\times \\text{GL}_2$. A key aspect is the computation of certain archimedean zeta integrals, whose $p$-adic counterparts are also studied in this note. This is crucially used in a sequel to this paper in order to construct a new $p$-adic $L$-function for $\\text{GSp}_4 \\times \\text{GL}_2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-28T16:31:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "archimedean zeta integrals",
      "gan-gross-prasad periods",
      "algebraicity results",
      "adic counterparts",
      "computation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}