{
  "id": "0811.1410",
  "version": "v3",
  "published": "2008-11-10T08:17:17.000Z",
  "updated": "2009-01-02T12:26:56.000Z",
  "title": "Conjectures about distinction and Asai $L$-functions of generic representations of general linear groups over local fields",
  "authors": [
    "Nadir Matringe"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $K/F$ be a quadratic extension of p-adic fields. The Bernstein-Zelevinsky's classification asserts that generic representations are parabolically induced from quasi-square-integrable representations. We show, following a method developed by Cogdell and Piatetski-Shapiro, that the equality of the Rankin-Selberg type Asai $L$-function of generic representations of $GL(n,K)$ and of the Asai $L$-function of the Langlands parameter, is equivalent to the truth of a conjecture about classification of distinguished generic representations in terms of the inducing quasi-square-integrable representations. As the conjecture is true for principal series representations, this gives the expression of the Asai L-function of such representations.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-01-02T12:26:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E50",
      "11S40"
    ],
    "keywords": [
      "generic representations",
      "general linear groups",
      "local fields",
      "conjecture",
      "distinction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0811.1410M"
    }
  }
}