{
  "id": "2108.01540",
  "version": "v1",
  "published": "2021-08-03T14:46:13.000Z",
  "updated": "2021-08-03T14:46:13.000Z",
  "title": "On the new identities of Dirichlet $L$-functions",
  "authors": [
    "Rong Ma",
    "Jinglei Zhang",
    "Yulong Zhang"
  ],
  "comment": "10 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $q\\ge3$ be an integer, $\\chi$ be a Dirichlet character modulo $q$, and $L(s,\\chi)$ denote the Dirichlet $L$-functions corresponding to $\\chi$. In this paper, we show some special function series, and give some new identities for the Dirichlet $L$-functions involving Gauss sums. Specially, we give specific identities for $L(2,\\chi)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-03T14:46:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M20",
      "F.2.0"
    ],
    "keywords": [
      "dirichlet character modulo",
      "special function series",
      "gauss sums",
      "specific identities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}