{
  "id": "2004.13644",
  "version": "v1",
  "published": "2020-04-28T16:38:23.000Z",
  "updated": "2020-04-28T16:38:23.000Z",
  "title": "A Divisor Formula and a Bound on the $\\mathbb{Q}$-gonality of the Modular Curve $X_1(N)$",
  "authors": [
    "Mark van Hoeij",
    "Hanson Smith"
  ],
  "comment": "18 pages. Appendix B summarizes notation. Comments are welcome!",
  "categories": [
    "math.NT"
  ],
  "abstract": "We give a formula for divisors of modular units on $X_1(N)$ and use it to prove that the $\\mathbb{Q}$-gonality of the modular curve $X_1(N)$ is bounded above by $\\left[\\frac{11N^2}{840}\\right]$, where $[\\bullet]$ denotes the nearest integer.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-28T16:38:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G16",
      "14H52",
      "11G05",
      "14G35",
      "11F03"
    ],
    "keywords": [
      "modular curve",
      "divisor formula",
      "modular units"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}