{
  "id": "1306.3711",
  "version": "v2",
  "published": "2013-06-16T22:51:44.000Z",
  "updated": "2013-06-20T08:10:34.000Z",
  "title": "Riemann Hypothesis: Architecture of a conjecture \"along\" the lines of Pólya. From trivial zeros and Harmonic Oscillator to information about non-trivial zeros of the Riemann zeta-function",
  "authors": [
    "Stefano Beltraminelli",
    "Danilo Merlini",
    "Sergey Sekatskii"
  ],
  "comment": "7 pages",
  "categories": [
    "math.NT",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We propose an architecture of a conjecture concerning the Riemann Hypothesis in the form of an \"alternative\" to the P\\'olya strategy: we construct a Hamiltonian H_Polya whose spectrum coincides exactly with that of the Harmonic Oscillator Hamiltonian H_osc if and only if the Riemann Hypothesis holds true. In other words, it can be said that we formulate the Riemann Hypothesis by means of a non-commutative structure on the real axis, viz., that of the Harmonic Oscillator, by an equation of the type H_Polya(H_osc) = H_osc: the Harmonic Oscillator operator, if viewed as an argument of H_Polya, reproduces itself.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-06-20T08:10:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M26"
    ],
    "keywords": [
      "non-trivial zeros",
      "riemann zeta-function",
      "conjecture",
      "architecture",
      "information"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1306.3711B"
    }
  }
}