{
  "id": "2001.04337",
  "version": "v1",
  "published": "2020-01-10T18:11:11.000Z",
  "updated": "2020-01-10T18:11:11.000Z",
  "title": "Congruences for coefficients of modular functions in levels 3, 5, and 7 with poles at 0",
  "authors": [
    "Paul Jenkins",
    "Ryan Keck"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1709.10189",
  "categories": [
    "math.NT"
  ],
  "abstract": "We give congruences modulo powers of $p \\in \\{3, 5,7\\}$ for the Fourier coefficients of certain modular functions in level $p$ with poles only at 0, answering a question posed by Andersen and the first author and continuing work done by the authors and Moss. The congruences involve a modulus that depends on the base $p$ expansion of the modular form's order of vanishing at $\\infty$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-10T18:11:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F30",
      "11F37"
    ],
    "keywords": [
      "modular functions",
      "congruences modulo powers",
      "modular forms order",
      "first author",
      "fourier coefficients"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}