{
  "id": "math/0210235",
  "version": "v1",
  "published": "2002-10-16T07:47:40.000Z",
  "updated": "2002-10-16T07:47:40.000Z",
  "title": "On strong multiplicity one for automorphic representations",
  "authors": [
    "C. S. Rajan"
  ],
  "comment": "8 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We extend the strong multiplicity one theorem of Jacquet, Piatetski-Shapiro and Shalika. Let $\\pi$ be a unitary, cuspidal, automorphic representation of $GL_n(\\A_K)$. Let $S$ be a set of finite places of $K$, such that the sum $\\sum_{v\\in S}Nv^{-2/(n^2+1)}$ is convergent. Then $\\pi$ is uniquely determined by the collection of the local components $\\{\\pi_v\\mid v\\not\\in S, ~v \\~\\text{finite}\\}$ of $\\pi$. Combining this theorem with base change, it is possible to consider sets $S$ of positive density, having appropriate splitting behavior with respect to solvable extensions of $K$, and where $\\pi$ is determined upto twisting by a character of the Galois group of $L$ over $K$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-10-16T07:47:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F70"
    ],
    "keywords": [
      "automorphic representation",
      "strong multiplicity",
      "galois group",
      "finite places",
      "local components"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math.....10235R"
    }
  }
}