{
  "id": "1401.4296",
  "version": "v2",
  "published": "2014-01-17T10:36:38.000Z",
  "updated": "2014-09-11T09:07:40.000Z",
  "title": "Values of twisted Artin $L$-functions",
  "authors": [
    "Kenneth Ward"
  ],
  "comment": "6 pages. minor changes. To appear in Archiv der Mathematik (2014)",
  "categories": [
    "math.NT"
  ],
  "abstract": "This note gives a simple proof that certain values of Artin's $L$-function, for a representation $\\rho$ with character $\\chi_\\rho$, are stable under twisting by an even Dirichlet character $\\chi$, up to an element generated over $\\mathbb Q$ by the values of $\\chi$ and $\\chi_\\rho$, and a product with a power of the Gauss sum $\\tau(\\chi)$ equal to the dimension of $\\rho$. This extends a result due to J. Coates and S. Lichtenbaum.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-01-17T10:36:38.000Z",
      "title": "Values of twists by Dirichlet characters of Artin $L$-functions",
      "comment": "8 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-09-11T09:07:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11L05",
      "11F67"
    ],
    "keywords": [
      "dirichlet character",
      "simple proof",
      "gauss sum",
      "representation",
      "lichtenbaum"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.4296W"
    }
  }
}