{
  "id": "2402.06572",
  "version": "v2",
  "published": "2024-02-09T17:45:21.000Z",
  "updated": "2024-07-08T08:44:59.000Z",
  "title": "Formal Siegel modular forms for arithmetic subgroups",
  "authors": [
    "Jan Hendrik Bruinier",
    "Martin Raum"
  ],
  "comment": "41 Pages",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "The notion of formal Siegel modular forms for an arithmetic subgroup $\\Gamma$ of the symplectic group of genus $n$ is a generalization of symmetric formal Fourier-Jacobi series. Assuming an upper bound on the affine covering number of the Siegel modular variety associated with $\\Gamma$, we prove that all formal Siegel modular forms are given by Fourier-Jacobi expansions of classical holomorphic Siegel modular forms. We also show that the required upper bound is always met if $2\\leq n \\leq 4$. As an application we consider the case of the paramodular group of squarefree level and genus $2$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-07-08T08:44:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F46",
      "11F50",
      "14G35",
      "14F06"
    ],
    "keywords": [
      "formal siegel modular forms",
      "arithmetic subgroup",
      "symmetric formal fourier-jacobi series",
      "upper bound",
      "classical holomorphic siegel modular forms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 41,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}