{
  "id": "1812.07863",
  "version": "v1",
  "published": "2018-12-19T10:23:53.000Z",
  "updated": "2018-12-19T10:23:53.000Z",
  "title": "Mean values of divisors of forms $n^2+Nm^2$",
  "authors": [
    "Peng Gao",
    "Liangyi Zhao"
  ],
  "comment": "18 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $N$ be any fixed positive integer and define \\begin{align*} S_N(x)=\\sum_{m, n \\leq x}d(n^2+Nm^2), \\end{align*} where $d(n)$ is the divisor function. We evaluate asymptotically $S_N(x)$ for several $N$, extending earlier works of Gafurov and Yu on the case $N=1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-19T10:23:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mean values",
      "divisor function",
      "extending earlier works",
      "fixed positive integer"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}