{
  "id": "1601.03622",
  "version": "v1",
  "published": "2016-01-14T15:26:36.000Z",
  "updated": "2016-01-14T15:26:36.000Z",
  "title": "Complete classification of 2-ramified power series",
  "authors": [
    "Jonas Fransson"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper we study lower ramification numbers of power series tangent to the identity that are defined over fields of positive characteristics $p$. Let $g$ be such a series, then $g$ has a fixed point at the origin and the corresponding lower ramification numbers of $g$ are then, up to a constant, the degree of the first non-linear term of $p$-power iterates of $g$. The result is a complete classification of power series $g$ having ramification numbers of the form ${2(1+p+\\dots+p^n)}$. Furthermore, in proving said classification we explicitly compute the first significant terms of $g$ at its $p$th iterate.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-14T15:26:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "complete classification",
      "study lower ramification numbers",
      "power series tangent",
      "first significant terms",
      "first non-linear term"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}