{
  "id": "1809.08623",
  "version": "v1",
  "published": "2018-09-23T16:11:31.000Z",
  "updated": "2018-09-23T16:11:31.000Z",
  "title": "The rings of Hilbert modular forms for $\\mathbb{Q}(\\sqrt{29})$ and $\\mathbb{Q}(\\sqrt{37})$",
  "authors": [
    "Brandon Williams"
  ],
  "comment": "18 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We use Borcherds products and their restrictions to Hirzebruch-Zagier curves to determine generators and relations for the graded rings of Hilbert modular forms for the fields $\\mathbb{Q}(\\sqrt{29})$ and $\\mathbb{Q}(\\sqrt{37})$. These seem to be the first cases where the graded ring can be computed despite obstructions to the existence of Borcherds products with arbitrary divisors.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-23T16:11:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F27",
      "11F41"
    ],
    "keywords": [
      "hilbert modular forms",
      "borcherds products",
      "hirzebruch-zagier curves",
      "determine generators",
      "arbitrary divisors"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}