{
  "id": "2008.11031",
  "version": "v1",
  "published": "2020-08-22T14:35:35.000Z",
  "updated": "2020-08-22T14:35:35.000Z",
  "title": "Thue inequalities with few coefficients",
  "authors": [
    "Paloma Bengoechea"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1906.03705",
  "journal": "International Mathematics Research Notices, rnaa136 (published 19 June 2020)",
  "doi": "10.1093/imrn/rnaa136",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $F(x, y)$ be a binary form with integer coefficients, degree $n\\geq 3$ and irreducible over the rationals. Suppose that only $s + 1$ of the $n + 1$ coefficients of $F$ are nonzero. We show that the Thue inequality $|F(x,y)|\\leq m$ has $\\ll sm^{2/n}$ solutions provided that the absolute value of the discriminant $D(F)$ of $F$ is large enough. We also give a new upper bound for the number of solutions of $|F(x,y)|\\leq m$, with no restriction on the discriminant of $F$ that depends mainly on $s$ and $m$, and slightly on $n$. Our bound becomes independent of $m$ when $m<|D(F)|^{2/(5(n-1))}$, and also independent of $n$ if $|D(F)|$ is large enough.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-22T14:35:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "thue inequality",
      "independent",
      "integer coefficients",
      "binary form",
      "absolute value"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}