{
  "id": "1106.0696",
  "version": "v1",
  "published": "2011-06-03T15:59:37.000Z",
  "updated": "2011-06-03T15:59:37.000Z",
  "title": "Counting points of fixed degree and given height over function fields",
  "authors": [
    "Jeffrey Lin Thunder",
    "Martin Widmer"
  ],
  "comment": "23 pages",
  "doi": "10.1112/blms/bds087",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $k$ be a finite field extension of the function field $\\bfF_p(T)$ and $\\bar{k}$ its algebraic closure. We count points in projective space $\\Bbb P ^{n-1}(\\bar{k})$ with given height and of fixed degree $d$ over the field $k$. If $n>2d+3$ we derive an asymptotic estimate for their number as the height tends to infinity. As an application we also deduce asymptotic estimates for certain decomposable forms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-06-03T15:59:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G50",
      "11G35"
    ],
    "keywords": [
      "function field",
      "fixed degree",
      "counting points",
      "finite field extension",
      "deduce asymptotic estimates"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1106.0696T"
    }
  }
}