{
  "id": "0905.4245",
  "version": "v3",
  "published": "2009-05-26T17:05:02.000Z",
  "updated": "2013-08-04T10:15:23.000Z",
  "title": "Spherical varieties and integral representations of L-functions",
  "authors": [
    "Yiannis Sakellaridis"
  ],
  "comment": "Appeared in Algebra & Number Theory, Vol. 6 (2012), No. 4, 611-667. Formula for subgroup H after example 4.5.1 missing from published version",
  "categories": [
    "math.NT",
    "math.RT"
  ],
  "abstract": "We present a conceptual and uniform interpretation of the methods of integral representations of L-functions (period integrals, Rankin-Selberg integrals). This leads to: (i) a way to classify of such integrals, based on the classification of certain embeddings of spherical varieties (whenever the latter is available), (ii) a conjecture which would imply a vast generalization of the method, and (iii) an explanation of the phenomenon of \"weight factors\" in a relative trace formula. We also prove results of independent interest, such as the generalized Cartan decomposition for spherical varieties of split groups over p-adic fields (following an argument of Gaitsgory and Nadler).",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-08-04T10:15:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F67"
    ],
    "keywords": [
      "spherical varieties",
      "integral representations",
      "l-functions",
      "period integrals",
      "rankin-selberg integrals"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0905.4245S"
    }
  }
}