{
  "id": "1310.4257",
  "version": "v5",
  "published": "2013-10-16T03:43:01.000Z",
  "updated": "2015-08-07T12:07:31.000Z",
  "title": "The (S,{2})-Iwasawa theory",
  "authors": [
    "Su Hu",
    "Min-Soo Kim"
  ],
  "comment": "15 Pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Iwasawa made the fundamental discovery that there is a close connection between the ideal class groups of $\\mathbb{Z}_{p}$-extensions of cyclotomic fields and the $p$-adic analogue of Riemann's zeta functions $$\\zeta(s)=\\sum_{n=1}^{\\infty}\\frac{1}{n^{s}}.$$ In this paper, we show that there may also exist a parallel Iwasawa's theory corresponding to the $p$-adic analogue of Euler's deformation of zeta functions $$\\phi(s)=\\sum_{n=1}^{\\infty}\\frac{(-1)^{n-1}}{n^{s}}.$$",
  "revisions": [
    {
      "version": "v4",
      "updated": "2014-07-30T03:44:51.000Z",
      "comment": "11 Pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v5",
      "updated": "2015-08-07T12:07:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R23",
      "11S40",
      "11S80"
    ],
    "keywords": [
      "adic analogue",
      "ideal class groups",
      "riemanns zeta functions",
      "close connection",
      "eulers deformation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.4257H"
    }
  }
}