{
  "id": "1207.4641",
  "version": "v2",
  "published": "2012-07-19T12:37:07.000Z",
  "updated": "2012-11-25T04:48:12.000Z",
  "title": "Arithmeticity for periods of automorphic forms",
  "authors": [
    "Wee Teck Gan",
    "A. Raghuram"
  ],
  "comment": "32 pages. The final version is to appear in the proceedings of the International Colloquium on Automorphic Representations and L-functions, held in TIFR, Mumbai, January 2012",
  "categories": [
    "math.NT",
    "math.RT"
  ],
  "abstract": "A cuspidal automorphic representation \\pi of a group G is said to to be distinguished with respect to a subgroup H if the integral of f along H is nonzero for a cusp form f in the space of \\pi. Such period integrals are related to (non)vanishing of interesting L-values and also to Langlands functoriality. This article discusses a general principle, labelled arithmeticity, which roughly states that \"\\pi is H-distinguished if and only if any Galois conjugate of \\pi is H-distinguished.\" We study this principle via several examples; starting with GL(2) and leading up to more complicated situations where the ambient group is a higher GL(n) or a classical group.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-11-25T04:48:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F67",
      "11F70",
      "11F75",
      "22E55"
    ],
    "keywords": [
      "automorphic forms",
      "arithmeticity",
      "cuspidal automorphic representation",
      "ambient group",
      "higher gl"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.4641T"
    }
  }
}