{
  "id": "math/0209204",
  "version": "v1",
  "published": "2002-09-16T23:03:37.000Z",
  "updated": "2002-09-16T23:03:37.000Z",
  "title": "Spectra of certain types of polynomials and tiling of integers with translates of finite sets",
  "authors": [
    "Sergei Konyagin",
    "Izabella Laba"
  ],
  "comment": "14 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We consider two number-theoretic problems arising from Fuglede's spectral set conjecture: characterizing finite sets that tile integers, and finding polynomials with (0,1) coefficients whose roots have a certain multiplicative structure. We verify several special cases of the relevant conjectures; in particular, we find necessary and sufficient conditions for a set A to tile the integers if A is a direct sum of cyclic subsets.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-09-16T23:03:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A99"
    ],
    "keywords": [
      "polynomials",
      "fugledes spectral set conjecture",
      "translates",
      "number-theoretic problems",
      "cyclic subsets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......9204K"
    }
  }
}