{
  "id": "1608.04146",
  "version": "v1",
  "published": "2016-08-14T22:18:56.000Z",
  "updated": "2016-08-14T22:18:56.000Z",
  "title": "Avoiding algebraic integers of bounded house in orbits of rational functions over cyclotomic closures",
  "authors": [
    "Evan Chen"
  ],
  "comment": "10 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $k$ be a number field with cyclotomic closure $k^{\\mathrm{cyc}}$, and let $h \\in k^{\\mathrm{cyc}}(x)$. For $A \\ge 1$ a real number, we show that \\[ \\{ \\alpha \\in k^{\\mathrm{cyc}} : h(\\alpha) \\in \\overline{\\mathbb Z} \\text{ has house at most } A \\} \\] is finite for many $h$. We also show that for many such $h$ the same result holds if $h(\\alpha)$ is replaced by orbits $h(h(\\cdots h(\\alpha)))$. This generalizes a result proved by Ostafe that concerns avoiding roots of unity, which is the case $A=1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-14T22:18:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R18",
      "37F10"
    ],
    "keywords": [
      "avoiding algebraic integers",
      "cyclotomic closure",
      "rational functions",
      "bounded house",
      "real number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}