{
  "id": "1211.5731",
  "version": "v2",
  "published": "2012-11-25T06:19:17.000Z",
  "updated": "2013-01-18T17:00:34.000Z",
  "title": "The circle method and bounds for $L$-functions - II: Subconvexity for twists of GL(3) $L$-functions",
  "authors": [
    "Ritabrata Munshi"
  ],
  "comment": "10 pages, revised version",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $\\pi$ be a $SL(3,\\mathbb Z)$ automorphic form. Let $\\chi=\\chi_1\\chi_2$ be a Dirichlet character with $\\chi_i$ primitive modulo $M_i$. Suppose $M_1$, $M_2$ are primes such that $\\sqrt{M_2}M^{4\\delta}<M_1<M_2M^{-3\\delta}$, where $M=M_1M_2$ and $0<\\delta<1/28$. In this paper we will prove the following subconvex bound $$ L(\\t1/2,\\pi\\otimes\\chi)\\ll_{\\pi,\\varepsilon} M^{3/4}-\\delta+\\varepsilon}. $$",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-01-18T17:00:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F66",
      "11M41"
    ],
    "keywords": [
      "circle method",
      "subconvexity",
      "automorphic form",
      "dirichlet character",
      "subconvex bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.5731M"
    }
  }
}