{
  "id": "1111.5600",
  "version": "v1",
  "published": "2011-11-23T19:54:58.000Z",
  "updated": "2011-11-23T19:54:58.000Z",
  "title": "On the Invariants of Towers of Function Fields over Finite Fields",
  "authors": [
    "Florian Hess",
    "Henning Stichtenoth",
    "Seher Tutdere"
  ],
  "comment": "23 pages",
  "doi": "10.1142/SO219498812501903",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We consider a tower of function fields F=(F_n)_{n\\geq 0} over a finite field F_q and a finite extension E/F_0 such that the sequence \\mathcal{E):=(EF_n)_{n\\goq 0} is a tower over the field F_q. Then we deal with the following: What can we say about the invariants of \\mathcal{E}; i.e., the asymptotic number of places of degree r for any r\\geq 1 in \\mathcal{E}, if those of F are known? We give a method based on explicit extensions for constructing towers of function fields over F_q with finitely many prescribed invariants being positive, and towers of function fields over F_q, for q a square, with at least one positive invariant and certain prescribed invariants being zero. We show the existence of recursive towers attaining the Drinfeld-Vladut bound of order r, for any r\\geq 1 with q^r a square. Moreover, we give some examples of recursive towers with all but one invariants equal to zero.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-11-23T19:54:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "function fields",
      "finite field",
      "prescribed invariants",
      "recursive towers",
      "asymptotic number"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1111.5600H"
    }
  }
}