{
  "id": "2011.10980",
  "version": "v1",
  "published": "2020-11-22T10:35:15.000Z",
  "updated": "2020-11-22T10:35:15.000Z",
  "title": "On a generalization of Menon-Sury identity to number fields involving a Dirichlet Character",
  "authors": [
    "Jaitra Chattopadhyay",
    "Subha Sarkar"
  ],
  "comment": "11 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "For every positive integer $n$, Sita Ramaiah's identity states that \\medskip \\begin{equation*} \\sum_{a_1, a_2, a_1+a_2 \\in (\\mathbb{Z}/n\\mathbb{Z})^*} \\gcd(a_1+a_2-1,n) = \\phi_2(n)\\sigma_0(n) \\; \\text{ where } \\; \\phi_2(n)= \\sum_{a_1, a_2, a_1+a_2 \\in (\\mathbb{Z}/n\\mathbb{Z})^*} 1, \\end{equation*} \\medskip where $(\\mathbb{Z}/n\\mathbb{Z})^*$ is the multiplicative group of units of the ring $\\mathbb{Z}/n\\mathbb{Z}$ and $\\sigma_s(n) = \\displaystyle\\sum_{d\\mid n}d^s$. \\smallskip This identity can also be viewed as a generalization of Menon's identity. In this article, we generalize this identity to an algebraic number field $K$ involving a Dirichlet character $\\chi$. Our result is a further generalization of a recent result in \\cite{wj} and \\cite{sury}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-22T10:35:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dirichlet character",
      "menon-sury identity",
      "generalization",
      "sita ramaiahs identity states",
      "algebraic number field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}