{
  "id": "1210.1216",
  "version": "v5",
  "published": "2012-10-03T20:00:02.000Z",
  "updated": "2013-07-16T12:02:41.000Z",
  "title": "Euler Products beyond the Boundary",
  "authors": [
    "Taro Kimura",
    "Shin-ya Koyama",
    "Nobushige Kurokawa"
  ],
  "comment": "16 pages, 20 figures; discussion in Sec. 3 extended; references added; figures and discussion added; references added",
  "journal": "Lett. Math. Phys. 104 (2014) 1-19",
  "doi": "10.1007/s11005-013-0644-3",
  "categories": [
    "math.NT",
    "cond-mat.stat-mech"
  ],
  "abstract": "We investigate the behavior of the Euler products of the Riemann zeta function and Dirichlet L-functions on the critical line. A refined version of the Riemann hypothesis, which is named \"the Deep Riemann Hypothesis\" (DRH), is examined. We also study various analogs for global function fields. We give an interpretation for the nontrivial zeros from the viewpoint of statistical mechanics.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2013-07-16T12:02:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M06"
    ],
    "keywords": [
      "euler products",
      "riemann zeta function",
      "global function fields",
      "deep riemann hypothesis",
      "dirichlet l-functions"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Letters in Mathematical Physics",
      "year": 2014,
      "month": "Jan",
      "volume": 104,
      "number": 1,
      "pages": 1
    },
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014LMaPh.104....1K"
    }
  }
}