{
  "id": "1309.1726",
  "version": "v1",
  "published": "2013-09-06T18:35:41.000Z",
  "updated": "2013-09-06T18:35:41.000Z",
  "title": "The distribution of values of short hybrid exponential sums on curves over finite fields",
  "authors": [
    "Kit-Ho Mak",
    "Alexandru Zaharescu"
  ],
  "comment": "20 pages",
  "journal": "Math. Res. Lett. 18 (2011), no. 01, 155--174",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $p$ be a prime number, $X$ be an absolutely irreducible affine plane curve over $\\mathbb{F}_p$, and $g,f\\in\\mathbb{F}_p(x,y)$. We study the distribution of the values of the hybrid exponential sums S_n on $n\\in\\mathcal{I}$ for some short interval $\\mathcal{I}$. We show that under some natural conditions the limiting distribution of the projections of the sum $S_n$, $n\\in\\mathcal{I}$ on any straight line through the origin is Gaussian as $p$ tends to infinity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-09-06T18:35:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G20",
      "11T23",
      "11T24"
    ],
    "keywords": [
      "short hybrid exponential sums",
      "finite fields",
      "distribution",
      "absolutely irreducible affine plane curve",
      "prime number"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.1726M"
    }
  }
}