{
  "id": "1606.05726",
  "version": "v1",
  "published": "2016-06-18T07:50:30.000Z",
  "updated": "2016-06-18T07:50:30.000Z",
  "title": "Hamiltonians arising from L-functions in the Selberg class",
  "authors": [
    "Masatoshi Suzuki"
  ],
  "categories": [
    "math.NT",
    "math.CA",
    "math.FA"
  ],
  "abstract": "We establish a new equivalent condition for the Grand Riemann Hypothesis for L-functions in a wide subclass of the Selberg class in terms of canonical systems of differential equations. A canonical system is determined by a real symmetric matrix valued function called a Hamiltonian. To establish the equivalent condition, we solve and use an inverse spectral problem for canonical systems of special type.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-18T07:50:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M41",
      "34A55",
      "11M26"
    ],
    "keywords": [
      "selberg class",
      "hamiltonians arising",
      "canonical system",
      "l-functions",
      "equivalent condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}