{
  "id": "2303.13785",
  "version": "v1",
  "published": "2023-03-24T03:52:33.000Z",
  "updated": "2023-03-24T03:52:33.000Z",
  "title": "An explicit upper bound for $L(1, χ)$ when $χ$ is quadratic",
  "authors": [
    "D. R. Johnston",
    "O. Ramare",
    "T. S. Trudgian"
  ],
  "comment": "17 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We consider Dirichlet $L$-functions $L(s, \\chi)$ where $\\chi$ is a non-principal quadratic character to the modulus $q$. We make explicit a result due to Pintz and Stephens by showing that $|L(1, \\chi)|\\leq \\frac{1}{2}\\log q$ for all $q\\geq 2\\cdot 10^{23}$ and $|L(1, \\chi)|\\leq \\frac{9}{20}\\log q$ for all $q\\geq 5\\cdot 10^{50}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-24T03:52:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M20"
    ],
    "keywords": [
      "explicit upper bound",
      "non-principal quadratic character"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}