{
  "id": "math/0510583",
  "version": "v1",
  "published": "2005-10-27T01:56:32.000Z",
  "updated": "2005-10-27T01:56:32.000Z",
  "title": "A Skolem-Mahler-Lech Theorem in Positive Characteristic and Finite Automata",
  "authors": [
    "Harm Derksen"
  ],
  "comment": "43 pages",
  "categories": [
    "math.NT",
    "math.AC"
  ],
  "abstract": "Lech proved in 1953 that the set of zeroes of a linear recurrence sequence in a field of characteristic 0 is the union of a finite set and finitely many infinite arithmetic progressions. This result is known as the Skolem-Mahler-Lech theorem. Lech gave a counterexample to a similar statement in positive characteristic. We will present some more pathological examples. We will state and prove a correct analog of the Skolem-Mahler-Lech theorem in positive characteristic. The zeroes of a recurrence sequence in positive characteristic can be described using finite automata.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-10-27T01:56:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B37",
      "11B85",
      "68Q70"
    ],
    "keywords": [
      "positive characteristic",
      "skolem-mahler-lech theorem",
      "finite automata",
      "linear recurrence sequence",
      "infinite arithmetic progressions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....10583D"
    }
  }
}