{
  "id": "2303.08391",
  "version": "v1",
  "published": "2023-03-15T06:45:35.000Z",
  "updated": "2023-03-15T06:45:35.000Z",
  "title": "The asymptotic formulae of sums of two smooth squares for divisor function",
  "authors": [
    "Nanxiang Wang",
    "Haobo Dai"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "A natural number $n$ is $y$-smooth if the greatest prime factor of $n$ does not exceed $y$. Let $s_{1}$ and $s_{2}$ are $y$-smooth numbers. We consider sums of smooth squares of the binary Titchmarsh divisor problem and give asymptotic formulae for $\\sum_{s_{1}^{2}+s_{2}^{2}\\le x}\\tau(s_{1}^{2}+s_{2}^{2}+1)$ for $(\\log x)^{K}\\le y<x^{\\frac{1}{2}}$, where $K$ is large enough.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-15T06:45:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "asymptotic formulae",
      "smooth squares",
      "divisor function",
      "binary titchmarsh divisor problem",
      "greatest prime factor"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}