{
  "id": "0811.4435",
  "version": "v1",
  "published": "2008-11-26T21:40:12.000Z",
  "updated": "2008-11-26T21:40:12.000Z",
  "title": "On the special values of certain Rankin-Selberg L-functions and applications to odd symmetric power L-functions of modular forms",
  "authors": [
    "A. Raghuram"
  ],
  "comment": "30 pages",
  "categories": [
    "math.NT",
    "math.RT"
  ],
  "abstract": "We prove an algebraicity result for the central critical value of certain Rankin-Selberg L-functions for GL(n) x GL(n-1). This is a generalization and refinement of some results of Harder, Kazhdan-Mazur-Schmidt, Mahnkopf, and Kasten-Schmidt. As an application of this result, we prove algebraicity results for certain critical values of the fifth and the seventh symmetric power L-functions attached to a holomorphic cusp form. Assuming Langlands functoriality one can prove similar algebraicity results for the special values of any odd symmetric power L-function. We also prove a conjecture of Blasius and Panchishkin on twisted L-values in some cases. We comment on the compatibility of our results with Deligne's conjecture on the critical values of motivic L-functions. These results, as in the above mentioned works, are, in general, based on a nonvanishing hypothesis on certain archimedean integrals.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-11-26T21:40:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F67",
      "11F70",
      "11F75",
      "22E55"
    ],
    "keywords": [
      "odd symmetric power l-function",
      "special values",
      "rankin-selberg l-functions",
      "modular forms",
      "symmetric power l-functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0811.4435R"
    }
  }
}