{
  "id": "1403.7079",
  "version": "v1",
  "published": "2014-03-27T15:26:11.000Z",
  "updated": "2014-03-27T15:26:11.000Z",
  "title": "On the non-vanishing of Dirichlet $L$-functions at the central point",
  "authors": [
    "Daniel Fiorilli"
  ],
  "comment": "11 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We investigate the consequences of natural conjectures of Montgomery type on the non-vanishing of Dirichlet $L$-functions at the central point. We first justify these conjectures using probabilistic arguments. We then show using a result of Bombieri, Friedlander and Iwaniec and a result of the author that they imply that almost all Dirichlet $L$-functions do not vanish at the central point. We also deduce a quantitative upper bound for the proportion of Dirichlet $L$-functions for which $L(\\frac 12,\\chi)=0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-03-27T15:26:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M20",
      "11M26",
      "11N13"
    ],
    "keywords": [
      "central point",
      "non-vanishing",
      "montgomery type",
      "natural conjectures",
      "probabilistic arguments"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1403.7079F"
    }
  }
}