{
  "id": "2310.18048",
  "version": "v1",
  "published": "2023-10-27T10:51:10.000Z",
  "updated": "2023-10-27T10:51:10.000Z",
  "title": "On the mean values of products of Dirichlet $L$-functions at positive integers",
  "authors": [
    "Yuan He"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, we study the mean value distributions of Dirichlet $L$-functions at positive integers. We give some explicit formulas for the mean values of products of two and three Dirichlet $L$-functions at positive integers weighted by Dirichlet characters that involve the Bernoulli functions. The results presented here are the generalizations of various known formulas.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-27T10:51:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "positive integers",
      "mean value distributions",
      "explicit formulas",
      "dirichlet characters",
      "bernoulli functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}