{
  "id": "1506.07416",
  "version": "v1",
  "published": "2015-06-24T15:13:27.000Z",
  "updated": "2015-06-24T15:13:27.000Z",
  "title": "Central limit theorem for Artin $L$-functions",
  "authors": [
    "Peter J. Cho",
    "Henry H. Kim"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We show that the sum of the traces of Frobenius elements of Artin $L$-functions in a family of $G$-fields satisfies the Gaussian distribution under certain counting conjectures. We prove the counting conjectures for $S_4$ and $S_5$-fields. We also show central limit theorem for modular form $L$-functions with the trivial central character with respect to congruence subgroups as the level goes to infinity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-24T15:13:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "central limit theorem",
      "trivial central character",
      "counting conjectures",
      "gaussian distribution",
      "frobenius elements"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150607416C"
    }
  }
}