{
  "id": "2007.05043",
  "version": "v1",
  "published": "2020-07-09T19:33:12.000Z",
  "updated": "2020-07-09T19:33:12.000Z",
  "title": "Subconvexity bound for $GL(3) \\times GL(2)$ $L$-functions in $GL(2)$ spectral aspect",
  "authors": [
    "Sumit Kumar"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $\\pi$ be a Hecke-Maass cusp form for $SL(3, \\mathbb{Z})$ and $f$ be a holomorphic cusp form with weight $k$ or Hecke-Maass cusp form corresponding to the Laplacian eigenvalue $1/4+k^2$, $k\\geq 1$ for $SL(2,\\mathbb{Z})$. In this paper, we prove the following subconvexity bound: L\\left(\\frac{1}{2}, \\pi \\times f\\right) \\ll_{\\pi,\\epsilon} k^{\\frac{3}{2}-\\frac{1}{51}+\\epsilon}, for the central values $L(1/2,\\pi \\times f)$ of the Rankin-Selberg $L$-function of $\\pi$ and $f$. Using the same method, by taking $\\pi$ to be the Eisenstein series, we also obtain the following subconvexity bound: L\\left( \\frac{1}{2},\\ f\\right) \\ll_{\\epsilon} k^{\\frac{1}{2}-\\frac{1}{153}+\\epsilon}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-09T19:33:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "subconvexity bound",
      "spectral aspect",
      "holomorphic cusp form",
      "hecke-maass cusp form corresponding",
      "laplacian eigenvalue"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}