{
  "id": "2305.19113",
  "version": "v1",
  "published": "2023-05-30T15:18:29.000Z",
  "updated": "2023-05-30T15:18:29.000Z",
  "title": "Algebracity and the $p$-adic Interpolation of Special $L$-values for certain Classical Groups",
  "authors": [
    "Yubo Jin"
  ],
  "comment": "64 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, we calculate the ramified local integrals in the doubling method and present an integral representation of standard $L$-functions for classical groups. We explicitly construct local sections of Eisenstein series such that the local ramified integrals represent certain ramified $L$-factors. As an application, we prove algebraicity of special $L$-values and construct $p$-adic $L$-functions for symplectic, unitary, quaternionic unitary and quaternionic orthogonal groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-30T15:18:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F67",
      "11F55"
    ],
    "keywords": [
      "classical groups",
      "adic interpolation",
      "algebracity",
      "quaternionic orthogonal groups",
      "explicitly construct local sections"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 64,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}