{
  "id": "0903.3591",
  "version": "v2",
  "published": "2009-03-20T19:12:49.000Z",
  "updated": "2010-03-09T12:27:24.000Z",
  "title": "The subconvexity problem for $\\GL_{2}$",
  "authors": [
    "Philippe Michel",
    "Akshay Venkatesh"
  ],
  "comment": "Almost final version to appear in Publ. Math IHES. References updated.",
  "journal": "Publ. Math IHES, 111 (2010), no. 1, 171-280",
  "doi": "10.1007/s10240-010-0025-8",
  "categories": [
    "math.NT"
  ],
  "abstract": "Generalizing and unifying prior results, we solve the subconvexity problem for the $L$-functions of $\\GL_{1}$ and $\\GL_{2}$ automorphic representations over a fixed number field, uniformly in all aspects. A novel feature of the present method is the softness of our arguments; this is largely due to a consistent use of canonically normalized period relations, such as those supplied by the work of Waldspurger and Ichino--Ikeda.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-03-09T12:27:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F66",
      "11F70"
    ],
    "keywords": [
      "subconvexity problem",
      "automorphic representations",
      "fixed number field",
      "unifying prior results",
      "novel feature"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0903.3591M"
    }
  }
}