{
  "id": "1806.05207",
  "version": "v1",
  "published": "2018-06-13T18:20:00.000Z",
  "updated": "2018-06-13T18:20:00.000Z",
  "title": "Interpolated sequences and critical $L$-values of modular forms",
  "authors": [
    "Robert Osburn",
    "Armin Straub"
  ],
  "comment": "23 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Recently, Zagier expressed an interpolated version of the Ap\\'ery numbers for $\\zeta(3)$ in terms of a critical $L$-value of a modular form of weight 4. We extend this evaluation in two directions. We first prove that interpolations of Zagier's six sporadic sequences are essentially critical $L$-values of modular forms of weight 3. We then establish an infinite family of evaluations between interpolations of leading coefficients of Brown's cellular integrals and critical $L$-values of modular forms of odd weight.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-13T18:20:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F03",
      "11M41"
    ],
    "keywords": [
      "modular form",
      "interpolated sequences",
      "browns cellular integrals",
      "sporadic sequences",
      "interpolations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}