{
  "id": "1210.1893",
  "version": "v1",
  "published": "2012-10-05T23:41:06.000Z",
  "updated": "2012-10-05T23:41:06.000Z",
  "title": "The number of roots of polynomials of large degree in a prime field",
  "authors": [
    "Amit Ghosh",
    "Kenneth Ward"
  ],
  "comment": "16 pages",
  "doi": "10.1093/imrn/rnt227",
  "categories": [
    "math.NT"
  ],
  "abstract": "We establish asymptotic upper bounds on the number of zeros modulo $p$ of certain polynomials with integer coefficients, with $p$ prime numbers arbitrarily large. The polynomials we consider have degree of size $p$ and are obtained by truncating certain power series with rational coefficients that satisfy simple differential equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-10-05T23:41:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11J81",
      "11G20",
      "11T23",
      "11T55"
    ],
    "keywords": [
      "large degree",
      "prime field",
      "polynomials",
      "satisfy simple differential equations",
      "establish asymptotic upper bounds"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.1893G"
    }
  }
}