{
  "id": "1812.04309",
  "version": "v1",
  "published": "2018-12-11T10:01:50.000Z",
  "updated": "2018-12-11T10:01:50.000Z",
  "title": "An arithmetical function related to Báez-Duarte's criterion for the Riemann hypothesis",
  "authors": [
    "Michel Balazard"
  ],
  "comment": "Harmonic Analysis and Applications (Michael Th. Rassias, ed.), In press",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this mainly expository article, we revisit some formal aspects of B{\\'a}ez-Duarte's criterion for the Riemann hypothesis. In particular, starting from Weingartner's formulation of the criterion, we define an arithmetical function $\\nu$, which is equal to the M{\\\"o}bius function if, and only if the Riemann hypothesis is true. We record the basic properties of the Dirichlet series of $\\nu$, and state a few questions. KEYWORDS: Riemann hypothesis, arithmetical functions, Dirichlet series, Hilbert space",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-11T10:01:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M26"
    ],
    "keywords": [
      "riemann hypothesis",
      "arithmetical function",
      "báez-duartes criterion",
      "dirichlet series",
      "expository article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}