{
  "id": "0901.0658",
  "version": "v2",
  "published": "2009-01-06T14:47:40.000Z",
  "updated": "2009-01-20T07:47:38.000Z",
  "title": "Higher Apery-like numbers arising from special values of the spectral zeta function for the non-commutative harmonic oscillator",
  "authors": [
    "Kazufumi Kimoto"
  ],
  "comment": "26 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "A generalization of the Apery-like numbers, which is used to describe the special values $\\zeta_Q(2)$ and $\\zeta_Q(3)$ of the spectral zeta function for the non-commutative harmonic oscillator, are introduced and studied. In fact, we give a recurrence relation for them, which shows a ladder structure among them. Further, we consider the `rational part' of the higher Apery-like numbers. We discuss several kinds of congruence relations among them, which are regarded as an analogue of the ones among Apery numbers.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-01-20T07:47:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M41",
      "11A07"
    ],
    "keywords": [
      "spectral zeta function",
      "non-commutative harmonic oscillator",
      "higher apery-like numbers arising",
      "special values",
      "apery numbers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0901.0658K"
    }
  }
}