{
  "id": "1602.03583",
  "version": "v1",
  "published": "2016-02-11T00:32:51.000Z",
  "updated": "2016-02-11T00:32:51.000Z",
  "title": "Divisor problem in arithmetic progressions modulo a prime power",
  "authors": [
    "Kui Liu",
    "Igor E. Shparlinski",
    "Tianping Zhang"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We obtain an asymptotic formula for the average value of the divisor function over the integers $n \\le x$ in an arithmetic progression $n \\equiv a \\pmod q$, where $q=p^k$ for a prime $p\\ge 3$ and a sufficiently large integer $k$. In particular, we break the classical barrier $q \\le x^{2/3}$ for such formulas, and generalise a recent result of R.~Khan (2015), making it uniform in $k$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-11T00:32:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "arithmetic progressions modulo",
      "prime power",
      "divisor problem",
      "divisor function",
      "average value"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160203583L"
    }
  }
}