{
  "id": "2010.10153",
  "version": "v1",
  "published": "2020-10-20T09:41:17.000Z",
  "updated": "2020-10-20T09:41:17.000Z",
  "title": "Subconvexity for $GL(3)\\times GL(2)$ $L$-functions in $GL(3)$ spectral aspect",
  "authors": [
    "Prahlad Sharma"
  ],
  "comment": "22 pages, Preliminary version. Comments welcome",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $f$ be a $SL(2,\\mathbb{Z})$ holomorhic Hecke form and $\\pi$ be a $SL(3,\\mathbb{Z})$ Maass cusp form with its Langlands parameter $\\mu$ in generic position i.e. away from Weyl chamber walls and away from self dual forms. We study the second moment $\\sum_{j} |L(1/2,\\pi_j\\times f)|^2$ and deduce the subconvexity bound \\begin{equation*} L(1/2,\\pi\\times f)\\ll_{f,\\epsilon} \\|\\mu\\|^{3/2-1/30+\\epsilon} \\end{equation*}",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-20T09:41:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "spectral aspect",
      "holomorhic hecke form",
      "maass cusp form",
      "self dual forms",
      "weyl chamber walls"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}