{
  "id": "2310.16508",
  "version": "v1",
  "published": "2023-10-25T09:51:18.000Z",
  "updated": "2023-10-25T09:51:18.000Z",
  "title": "Hermitian Jacobi Forms Having Modules as their Index and Vector-Valued Jacobi Forms",
  "authors": [
    "Shaul Zemel"
  ],
  "comment": "60 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We develop the theory of Hermitian Jacobi forms of lattice index, for both definite and indefinite Hermitian lattices. We also prove a theta decomposition theorem for vector-valued Jacobi forms (both in the orthogonal and Hermitian settings), with enhanced periodicity properties. This allows us to give a good definition of orthogonal and Hermitian Jacobi forms of matrix index, when the matrix need not be integral in any natural sense.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-25T09:51:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F50",
      "11F27",
      "11F37"
    ],
    "keywords": [
      "hermitian jacobi forms",
      "vector-valued jacobi forms",
      "indefinite hermitian lattices",
      "theta decomposition theorem",
      "lattice index"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 60,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}