{
  "id": "2407.05583",
  "version": "v1",
  "published": "2024-07-08T03:36:45.000Z",
  "updated": "2024-07-08T03:36:45.000Z",
  "title": "The Ranking-Selberg integral on ${\\bf GSp(2)}$ for square free levels",
  "authors": [
    "Seiji Kuga",
    "Masao Tsuzuki"
  ],
  "comment": "45 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We explicitly compute the Rankin-Selberg type integral introduced by Piatetski-Shapiro over adeles for vector-valued Siegel cusp forms of square-free levels $\\Gamma_0(N)$. On the way, for particular test functions in the Bessel models of irreducible admissible representations, exact evaluations of the local zeta-integrals are given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-08T03:36:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F46",
      "11F67"
    ],
    "keywords": [
      "square free levels",
      "ranking-selberg integral",
      "vector-valued siegel cusp forms",
      "rankin-selberg type integral",
      "square-free levels"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 45,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}