{
  "id": "2006.02291",
  "version": "v1",
  "published": "2020-06-03T14:20:35.000Z",
  "updated": "2020-06-03T14:20:35.000Z",
  "title": "The classification of free algebras of orthogonal modular forms",
  "authors": [
    "Haowu Wang"
  ],
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We prove a necessary and sufficient condition for the graded algebra of automorphic forms on a symmetric domain of type IV to be free. From the necessary condition, we derive a classification result. Let $M$ be an even lattice of signature $(2,n)$ splitting two hyperbolic planes. Suppose $\\Gamma$ is a subgroup of the integral orthogonal group of $M$ containing the discriminant kernel. It is proved that there are exactly 26 groups $\\Gamma$ such that the space of modular forms for $\\Gamma$ is a free algebra. Using the sufficient condition, we recover some well-known results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-03T14:20:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F55",
      "51F15",
      "32N15"
    ],
    "keywords": [
      "orthogonal modular forms",
      "free algebra",
      "classification",
      "sufficient condition",
      "integral orthogonal group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}