{
  "id": "2105.07422",
  "version": "v2",
  "published": "2021-05-16T12:48:57.000Z",
  "updated": "2024-04-26T14:39:28.000Z",
  "title": "More than 60% of zeros of Dirichlet $L$-functions are on the critical line",
  "authors": [
    "Keiju Sono"
  ],
  "comment": "Comments are always welcomed",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, we estimate the proportion of zeros of Dirichlet $L$-functions on the critical line. Using Feng's mollifier and an asymptotic formula for the mean square of Dirichlet $L$-functions, we prove that averaged over primitive characters and conductors, at least 61.07 % of zeros of Dirichlet $L$-functions are on the critical line, and at least 60.44 % of zeros are simple and on the critical line. These results improve the work of Conrey, Iwaniec and Soundararajan.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-04-26T14:39:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M06"
    ],
    "keywords": [
      "critical line",
      "mean square",
      "asymptotic formula",
      "fengs mollifier",
      "primitive characters"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}