{
  "id": "1310.8564",
  "version": "v2",
  "published": "2013-10-31T15:56:55.000Z",
  "updated": "2014-10-29T16:02:04.000Z",
  "title": "Estimates for spectral density functions of matrices over C[Z^d]",
  "authors": [
    "Wolfgang Lueck"
  ],
  "comment": "11 pages, to appear in Annales Mathematiques Blaise Pascal, final version. We have taken out in the earlier version the algorithm for computing the Mahler measure since there are better ones in the literature",
  "categories": [
    "math.NT"
  ],
  "abstract": "We give a polynomial bound on the spectral density function of a matrix over the complex group ring of Z^d. It yields an explicit lower bound on the Novikov-Shubin invariant associated to this matrix showing in particular that the Novikov-Shubin invariant is larger than zero.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-10-31T15:56:55.000Z",
      "title": "A recipe to compute Mahler measures",
      "abstract": "We give an algorithm to compute the Mahler measure of a polynomial which does only depend on the coefficients, does not need any informations about the roots, and comes with an explicit estimate of the error term. We also prove the positivity of the Novikov-Shubin invariants for matrices over the complex group ring of Z^d.",
      "comment": "14 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-10-29T16:02:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R06",
      "46L99",
      "58J52"
    ],
    "keywords": [
      "mahler measure",
      "explicit estimate",
      "error term",
      "novikov-shubin invariants",
      "informations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.8564L"
    }
  }
}