{
  "id": "1704.02498",
  "version": "v1",
  "published": "2017-04-08T14:19:28.000Z",
  "updated": "2017-04-08T14:19:28.000Z",
  "title": "Explicit upper bound for the average number of divisors of irreducible quadratic polynomials",
  "authors": [
    "Kostadinka Lapkova"
  ],
  "comment": "Improves the result in arXiv:1509.08243, 11 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Consider the divisor sum $\\sum_{n\\leq N}\\tau(n^2+2bn+c)$ for integers $b$ and $c$. We extract an asymptotic formula for the average divisor sum in a convenient form, and provide an explicit upper bound for this sum with the correct main term. As an application we give an improvement of the maximal possible number of $D(-1)$-quadruples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-08T14:19:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "explicit upper bound",
      "irreducible quadratic polynomials",
      "average number",
      "average divisor sum",
      "correct main term"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}