{
  "id": "2003.08157",
  "version": "v1",
  "published": "2020-03-18T11:09:59.000Z",
  "updated": "2020-03-18T11:09:59.000Z",
  "title": "$p$-adic Polylogarithms and $p$-adic Hecke $L$-functions for Totally Real Fields",
  "authors": [
    "Kenichi Bannai",
    "Kei Hagihara",
    "Kazuki Yamada",
    "Shuji Yamamoto"
  ],
  "comment": "32 pages",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "The purpose of this article is to newly define the $p$-adic polylogarithm as an equivariant class in the cohomology of a certain infinite disjoint union of algebraic tori associated to a totally real field. We will then express the special values of $p$-adic $L$-functions interpolating nonpositive values of Hecke $L$-functions of the totally real field in terms of special values of these $p$-adic polylogarithms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-18T11:09:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M35",
      "11R80",
      "11R42",
      "14L15"
    ],
    "keywords": [
      "totally real field",
      "adic polylogarithm",
      "adic hecke",
      "special values",
      "infinite disjoint union"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}