{
  "id": "1311.6120",
  "version": "v2",
  "published": "2013-11-24T13:44:56.000Z",
  "updated": "2014-02-16T14:20:10.000Z",
  "title": "The circle method and bounds for $L$-functions - IV: Subconvexity for twists of $GL(3)$ $L$-functions - B",
  "authors": [
    "Ritabrata Munshi"
  ],
  "comment": "Second draft: 36 pages, several minor errors corrected",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $\\pi$ be a $SL(3,\\mathbb Z)$ Hecke-Maass cusp form satisfying the Ramanujan conjecture and the Selberg-Ramanujan conjecture, and let $\\chi$ be a primitive Dirichlet character modulo $M$, which we assume to be prime for simplicity. We will prove the following subconvex bound $$ L\\left(\\tfrac{1}{2},\\pi\\otimes\\chi\\right)\\ll_{\\pi,\\varepsilon} M^{\\frac{3}{4}-\\frac{1}{1612}+\\varepsilon}. $$",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-02-16T14:20:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "circle method",
      "subconvexity",
      "primitive dirichlet character modulo",
      "hecke-maass cusp form satisfying",
      "selberg-ramanujan conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1311.6120M"
    }
  }
}