{
  "id": "1604.08000",
  "version": "v1",
  "published": "2016-04-27T09:52:35.000Z",
  "updated": "2016-04-27T09:52:35.000Z",
  "title": "Twists of $GL(3)$ $L$-functions",
  "authors": [
    "Ritabrata Munshi"
  ],
  "comment": "First draft",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $\\pi$ be a $SL(3,\\mathbb Z)$ Hecke-Maass cusp form, and let $\\chi$ be a primitive Dirichlet character modulo $M$, which we assume to be prime. In this note we revisit the subconvexity problem addressed in `The circle method and bounds for $L$-functions IV' and establish the following unconditional bound \\begin{align*} L\\left(\\tfrac{1}{2},\\pi\\otimes\\chi\\right)\\ll M^{3/4-1/308+\\varepsilon}. \\end{align*}",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-27T09:52:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F66"
    ],
    "keywords": [
      "hecke-maass cusp form",
      "primitive dirichlet character modulo",
      "circle method",
      "subconvexity problem",
      "unconditional bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160408000M"
    }
  }
}