{
  "id": "1203.6689",
  "version": "v3",
  "published": "2012-03-30T00:17:48.000Z",
  "updated": "2012-07-11T19:44:55.000Z",
  "title": "Shintani cocycles and vanishing order of $p$-adic Hecke $L$-series at $s=0$",
  "authors": [
    "Michael Spiess"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $\\chi$ be a Hecke character of finite order of a totally real number field $F$. By using Hill's Shintani cocyle we provide a cohomological construction of the $p$-adic $L$-series $L_p(\\chi, s)$ associated to $\\chi$. This is used to show that $L_p(\\chi, s)$ has a trivial zero at $s=0$ of order at least equal to the number of places of $F$ above $p$ where the local component of $\\chi$ is trivial.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-07-11T19:44:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "adic hecke",
      "shintani cocycles",
      "vanishing order",
      "hills shintani cocyle",
      "totally real number field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1203.6689S"
    }
  }
}