{
  "id": "1609.08100",
  "version": "v1",
  "published": "2016-09-26T18:02:34.000Z",
  "updated": "2016-09-26T18:02:34.000Z",
  "title": "On Divisors of Modular Forms",
  "authors": [
    "Kathrin Bringmann",
    "Ben Kane",
    "Steffen Löbrich",
    "Ken Ono",
    "Larry Rolen"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "The denominator formula for the Monster Lie algebra is the product expansion for the modular function $j(z)-j(\\tau)$ given in terms of the Hecke system of $\\operatorname{SL}_2(\\mathbb Z)$-modular functions $j_n(\\tau)$. It is prominent in Zagier's seminal paper on traces of singular moduli, and in the Duncan-Frenkel work on Moonshine. The formula is equivalent to the description of the generating function for the $j_n(z)$ as a weight 2 modular form with a pole at $z$. Although these results rely on the fact that $X_0(1)$ has genus 0, here we obtain a generalization, framed in terms of polar harmonic Maass forms, for all of the $X_0(N)$ modular curves. We use these functions to study divisors of modular forms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-26T18:02:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F03",
      "11F37",
      "11F30"
    ],
    "keywords": [
      "modular form",
      "polar harmonic maass forms",
      "modular function",
      "monster lie algebra",
      "zagiers seminal paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}