{
  "id": "2006.12546",
  "version": "v1",
  "published": "2020-06-16T23:32:23.000Z",
  "updated": "2020-06-16T23:32:23.000Z",
  "title": "On the zeros of Dirichlet L-functions",
  "authors": [
    "Tatenda Isaac Kubalalika"
  ],
  "comment": "4 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $\\chi$ be a Dirichlet character. Define $\\Theta_\\chi$ to be the supremum of the real parts of the zeros of the corresponding Dirichlet L-function $L(s, \\chi)$. We demonstrate in this note that $\\Theta_{\\chi} < 1$ for all $\\chi$. A particular corollary of our result would be an improved error bound for the Prime Number Theorem for arithmetic progressions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-16T23:32:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M26",
      "11M06"
    ],
    "keywords": [
      "prime number theorem",
      "corresponding dirichlet l-function",
      "real parts",
      "dirichlet character",
      "error bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}