{
  "id": "2506.16083",
  "version": "v1",
  "published": "2025-06-19T07:11:20.000Z",
  "updated": "2025-06-19T07:11:20.000Z",
  "title": "On the vanishing order of Jacobi forms at infinity",
  "authors": [
    "Jialin Li",
    "Haowu Wang"
  ],
  "comment": "20 pages, comments welcome!",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, we establish two types of upper bounds on the vanishing order of Jacobi forms at infinity. The first type is for classical Jacobi forms, which is optimal in a certain sense. The second type is for Jacobi forms of lattice index. Based on this bound, we obtain a lower bound on the slope of orthogonal modular forms, and we prove that the module of symmetric formal Fourier--Jacobi series on $\\mathrm{O}(m,2)$ has finite rank.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-06-19T07:11:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F46",
      "11F50",
      "11F55"
    ],
    "keywords": [
      "vanishing order",
      "symmetric formal fourier-jacobi series",
      "orthogonal modular forms",
      "classical jacobi forms",
      "finite rank"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}