{
  "id": "1510.08086",
  "version": "v1",
  "published": "2015-10-27T20:26:55.000Z",
  "updated": "2015-10-27T20:26:55.000Z",
  "title": "Explicit results on the distribution of zeros of Hecke $L$-functions",
  "authors": [
    "Jesse Thorner",
    "Asif Zaman"
  ],
  "comment": "32 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We prove an explicit log-free zero density estimate and an explicit version of the zero-repulsion phenomenon of Deuring and Heilbronn for Hecke $L$-functions. In forthcoming work of the second author, these estimates will be used to establish explicit bounds on the least norm of a prime ideal in a congruence class group and improve upon existing explicit bounds for the least norm of a prime ideal in the Chebotarev density theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-27T20:26:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R42",
      "11N36",
      "11R44"
    ],
    "keywords": [
      "explicit results",
      "explicit log-free zero density estimate",
      "distribution",
      "prime ideal",
      "explicit bounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151008086T"
    }
  }
}