{
  "id": "1402.0120",
  "version": "v4",
  "published": "2014-02-01T20:00:35.000Z",
  "updated": "2015-05-26T09:49:50.000Z",
  "title": "Arithmetic of positive characteristic L-series values in Tate algebras",
  "authors": [
    "Bruno Angles",
    "Federico Pellarin",
    "Floric Tavares-Ribeiro"
  ],
  "comment": "final version",
  "categories": [
    "math.NT"
  ],
  "abstract": "The second author has recently introduced a new class of L-series in the arithmetic theory of function fields over finite fields. We show that the value at one of these L-series encode arithmetic informations of certain Drinfeld modules defined over Tate algebras. This enables us to generalize Anderson's log-algebraicity Theorem and Taelman's Herbrand-Ribet Theorem.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-05-18T19:15:13.000Z",
      "comment": "minor corrections. added Section 10 with connection with the theory of global L-series",
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2015-05-26T09:49:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "positive characteristic l-series values",
      "tate algebras",
      "l-series encode arithmetic informations",
      "generalize andersons log-algebraicity theorem",
      "taelmans herbrand-ribet theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1402.0120A"
    }
  }
}