{
  "id": "1212.4348",
  "version": "v1",
  "published": "2012-12-18T13:36:36.000Z",
  "updated": "2012-12-18T13:36:36.000Z",
  "title": "On partial sums of the Möbius and Liouville functions for number fields",
  "authors": [
    "Yusuke Fujisawa",
    "Makoto Minamide"
  ],
  "comment": "13 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Landau examined the partial sums of the M\\\"obius function and the Liouville function for a number field $K$. First we shall try again the same problem by using a new Perron's formula due to Liu and Ye. Next we consider the equivalent theorem of the grand Riemann hypothesis for the Dedekind zeta-function of $K$ and that of the prime ideal theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-12-18T13:36:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A25",
      "11R42"
    ],
    "keywords": [
      "partial sums",
      "number field",
      "liouville function",
      "prime ideal theorem",
      "grand riemann hypothesis"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1212.4348F"
    }
  }
}