{
  "id": "1902.01102",
  "version": "v1",
  "published": "2019-02-04T09:47:40.000Z",
  "updated": "2019-02-04T09:47:40.000Z",
  "title": "On Cilleruelo's conjecture for the least common multiple of polynomial sequences",
  "authors": [
    "Zeév Rudnick",
    "Sa'ar Zehavi"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "A conjecture due to Cilleruelo states that for an irreducible polynomial $f$ with integer coefficients of degree $d\\geq 2$, the least common multiple $L_f(N)$ of the sequence $f(1), f(2), \\dots, f(N)$ has asymptotic growth $\\log L_f(N)\\sim (d-1)N\\log N$ as $N\\to \\infty$. We establish a version of this conjecture for almost all shifts of a fixed polynomial, the range of $N$ depending on the range of shifts.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-04T09:47:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11N37"
    ],
    "keywords": [
      "common multiple",
      "cilleruelos conjecture",
      "polynomial sequences",
      "asymptotic growth",
      "integer coefficients"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}