{
  "id": "math-ph/0605066",
  "version": "v1",
  "published": "2006-05-24T18:26:17.000Z",
  "updated": "2006-05-24T18:26:17.000Z",
  "title": "Zeros of sections of exponential sums",
  "authors": [
    "Pavel Bleher",
    "Robert Mallison",
    "jr"
  ],
  "comment": "35 pages, 5 figures",
  "categories": [
    "math-ph",
    "math.CA",
    "math.MP"
  ],
  "abstract": "We derive the large $n$ asymptotics of zeros of sections of a generic exponential sum. We divide all the zeros of the $n$-th section of the exponential sum into ``genuine zeros'', which approach, as $n\\to\\infty$, the zeros of the exponential sum, and ``spurious zeros'', which go to infinity as $n\\to\\infty$. We show that the spurious zeros, after scaling down by the factor of $n$, approach a ``rosette'', a finite collection of curves on the complex plane, resembling the rosette. We derive also the large $n$ asymptotics of the ``transitional zeros'', the intermediate zeros between genuine and spurious ones. Our results give an extension to the classical results of Szeg\\\"o about the large $n$ asymptotics of zeros of sections of the exponential, sine, and cosine functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-05-24T18:26:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30D20",
      "30E10"
    ],
    "keywords": [
      "asymptotics",
      "generic exponential sum",
      "spurious zeros",
      "cosine functions",
      "th section"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.ph...5066B"
    }
  }
}