{
  "id": "1810.13257",
  "version": "v1",
  "published": "2018-10-30T02:08:10.000Z",
  "updated": "2018-10-30T02:08:10.000Z",
  "title": "Low-lying zeros of L-functions for Quaternion Algebras",
  "authors": [
    "Didier Lesesvre"
  ],
  "comment": "28 pages. arXiv admin note: text overlap with arXiv:1810.02787",
  "categories": [
    "math.NT"
  ],
  "abstract": "The density conjecture of Katz and Sarnak predicts that, for natural families of L-functions, the distribution of zeros lying near the real axis is governed by a group of symmetry. In the case of the universal family of automorphic forms of bounded analytic conductor on a totally definite quaternion algebra, we determine the associated distribution for a restricted class of test functions. In particular it leads to non-trivial results on densities of non-vanishing at the central point.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-30T02:08:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M26",
      "11F70"
    ],
    "keywords": [
      "low-lying zeros",
      "l-functions",
      "totally definite quaternion algebra",
      "distribution",
      "real axis"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}