{
  "id": "1607.01566",
  "version": "v1",
  "published": "2016-07-06T11:18:33.000Z",
  "updated": "2016-07-06T11:18:33.000Z",
  "title": "The bundle Laplacian on discrete tori",
  "authors": [
    "Fabien Friedli"
  ],
  "comment": "20 pages",
  "categories": [
    "math.CO",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We prove an asymptotic formula for the determinant of the bundle Laplacian on discrete $d$-dimensional tori as the number of vertices tends to infinity. This determinant has a combinatorial interpretation in terms of cycle-rooted spanning forests. We also establish a relation (in the limit) between the spectral zeta function of a line bundle over a discrete torus, the spectral zeta function of the infinite graph $\\mathbb{Z}^d$ and the Epstein-Hurwitz zeta function. The latter can be viewed as the spectral zeta function of the twisted continuous torus which is the limit of the sequence of discrete tori.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-06T11:18:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "discrete torus",
      "bundle laplacian",
      "spectral zeta function",
      "epstein-hurwitz zeta function",
      "vertices tends"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}