{
  "id": "1312.4053",
  "version": "v1",
  "published": "2013-12-14T15:00:23.000Z",
  "updated": "2013-12-14T15:00:23.000Z",
  "title": "Refined class number formulas for $\\mathbb{G}_m$",
  "authors": [
    "Barry Mazur",
    "Karl Rubin"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We formulate a generalization of a `refined class number formula' of Darmon. Our conjecture deals with Stickelberger-type elements formed from generalized Stark units, and has two parts: the `order of vanishing' and the `leading term'. Using the theory of Kolyvagin systems we prove a large part of this conjecture when the order of vanishing of the corresponding complex $L$-function is $1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-12-14T15:00:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R42",
      "11R27",
      "11R23"
    ],
    "keywords": [
      "refined class number formula",
      "conjecture deals",
      "stickelberger-type elements",
      "generalized stark units",
      "kolyvagin systems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.4053M"
    }
  }
}