{
  "id": "1201.1585",
  "version": "v5",
  "published": "2012-01-07T20:53:16.000Z",
  "updated": "2013-05-23T15:01:06.000Z",
  "title": "On automorphic L-functions in positive characteristic",
  "authors": [
    "Luis Alberto Lomelí"
  ],
  "comment": "Earlier versions of the paper have an appendix \"Uniqueness of Rankin-Selberg products\" by G. Henniart and L. A. Lomel\\'i. The appendix was rewritten and is now a separate independent paper",
  "categories": [
    "math.NT"
  ],
  "abstract": "We give a proof of the existence of Asai, exterior square, and symmetric square local $L$-functions, $\\gamma$-factors and root numbers in characteristic $p$, including the case of $p = 2$. Our study is made possible by developing the Langlands-Shahidi method over a global function field in the case of a Siegel Levi subgroup of a split classical group or a quasi-split unitary group. The resulting automorphic $L$-functions are shown to satisfy a rationality property and a functional equation. A uniqueness result of the author and G. Henniart allows us to show that the definitions provided in this article are in accordance with the local Langlands conjecture for ${\\rm GL}_n$. Furthermore, in order to be self contained, we include a treatise of $L$-functions arising from maximal Levi subgroups of general linear groups.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2013-05-23T15:01:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F70",
      "11M38",
      "22E50",
      "22E55"
    ],
    "keywords": [
      "automorphic l-functions",
      "positive characteristic",
      "general linear groups",
      "global function field",
      "maximal levi subgroups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1201.1585L"
    }
  }
}