{
  "id": "2003.05374",
  "version": "v1",
  "published": "2020-03-11T15:47:54.000Z",
  "updated": "2020-03-11T15:47:54.000Z",
  "title": "On some free algebras of orthogonal modular forms",
  "authors": [
    "Haowu Wang",
    "Brandon Williams"
  ],
  "comment": "Comments are welcome!",
  "categories": [
    "math.NT"
  ],
  "abstract": "For 25 orthogonal groups of signature $(2,n)$ related to the root lattices $A_1$, $2A_1$, $3A_1$, $4A_1$, $A_2$, $A_3$, $A_4$, $A_5$, $A_6$, $A_7$, $D_4$, $D_5$, $D_6$, $D_7$, $D_8$, $E_6$, $E_7$, we prove that the algebras of modular forms on symmetric domains of type IV are freely generated by the additive lifts of some special Jacobi forms. The proof is universal and elementary.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-11T15:47:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F50",
      "11F55"
    ],
    "keywords": [
      "orthogonal modular forms",
      "free algebras",
      "special jacobi forms",
      "root lattices",
      "orthogonal groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}