{
  "id": "2001.05782",
  "version": "v1",
  "published": "2020-01-16T13:14:38.000Z",
  "updated": "2020-01-16T13:14:38.000Z",
  "title": "An explicit upper bound for Siegel zeros of imaginary quadratic fields",
  "authors": [
    "Dimbinaina Ralaivaosaona",
    "Faratiana Brice Razakarinoro"
  ],
  "comment": "21 pages, 2 figures",
  "categories": [
    "math.NT"
  ],
  "abstract": "For any integer $d\\geq 3$ such that $-d$ is a fundamental discriminant, we show that the Dirichlet $L$-function associated with the real primitive character $\\chi(\\cdot)=(\\frac{-d}{\\cdot})$ does not vanish on the positive part of the interval $[1-6.5/\\sqrt{d},\\ 1]. $",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-16T13:14:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M20"
    ],
    "keywords": [
      "explicit upper bound",
      "imaginary quadratic fields",
      "siegel zeros",
      "fundamental discriminant",
      "real primitive character"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}