{
  "id": "math/0601479",
  "version": "v2",
  "published": "2006-01-19T18:50:04.000Z",
  "updated": "2006-06-21T19:45:15.000Z",
  "title": "Interpolation of numbers of Catalan type in a local field of positive characteristic",
  "authors": [
    "Greg W. Anderson"
  ],
  "comment": "LaTeX, 50 pages. v2: Introduction and last section rewritten, otherwise only some typos corrected. This is the final version, to appear in Crelle",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $k$ be a local field of positive characteristic. Let $L$ be a cocompact discrete subgroup of $k$. Let $U$ be an open compact subgroup of $k$. Let $\\ell$, $u$ and $a$ be elements of $k$, with $a$ nonzero. We study the behavior of the product $\\prod_{0\\neq x\\in (\\ell+L)\\cap a(u+U)}x$ as $a$ varies. Our main result, which blends harmonic analysis and local class field theory, provides local confirmation of a conjecture concerning global function fields recently made by the author (math.NT/0407535).",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-06-21T19:45:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11S31",
      "11S80"
    ],
    "keywords": [
      "local field",
      "positive characteristic",
      "catalan type",
      "interpolation",
      "conjecture concerning global function fields"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 50,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......1479A"
    }
  }
}