{
  "id": "1601.06512",
  "version": "v1",
  "published": "2016-01-25T08:46:33.000Z",
  "updated": "2016-01-25T08:46:33.000Z",
  "title": "Hardy's function $Z(t)$ - results and problems",
  "authors": [
    "Aleksandar Ivić"
  ],
  "comment": "15 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "This is primarily an overview article on some results and problems involving the classical Hardy function $$ Z(t) := \\zeta(1/2+it){\\bigl(\\chi(1/2+it)\\bigr)}^{-1/2}, \\quad \\zeta(s) = \\chi(s)\\zeta(1-s). $$ In particular, we discuss the first and third moment of $Z(t)$ (with and without shifts) and the distribution of its positive and negative values. A new result involving the distribution of its values is presented.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-25T08:46:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M06"
    ],
    "keywords": [
      "hardys function",
      "distribution",
      "classical hardy function",
      "overview article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160106512I"
    }
  }
}