{
  "id": "1101.0142",
  "version": "v2",
  "published": "2010-12-30T19:35:09.000Z",
  "updated": "2014-07-01T20:17:29.000Z",
  "title": "Asymptotic Improvements of Lower Bounds for the Least Common Multiples of Arithmetic Progressions",
  "authors": [
    "Daniel M. Kane",
    "Scott D. Kominers"
  ],
  "comment": "10 pages",
  "doi": "10.4153/CMB-2014-017-0",
  "categories": [
    "math.NT"
  ],
  "abstract": "For relatively prime positive integers $u_0$ and $r$, we consider the least common multiple $L_n:=\\mathrm{lcm}(u_0,u_1,\\ldots, u_n)$ of the finite arithmetic progression $\\{u_k:=u_0+kr\\}_{k=0}^n$. We derive new lower bounds on $L_n$ which improve upon those obtained previously when either $u_0$ or $n$ is large. When $r$ is prime, our best bound is sharp up to a factor of $n+1$ for $u_0$ properly chosen, and is also nearly sharp as $n\\to\\infty$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-07-01T20:17:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A05"
    ],
    "keywords": [
      "lower bounds",
      "common multiple",
      "asymptotic improvements",
      "finite arithmetic progression",
      "relatively prime positive integers"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1101.0142K"
    }
  }
}