{
  "id": "1810.00539",
  "version": "v1",
  "published": "2018-10-01T06:01:12.000Z",
  "updated": "2018-10-01T06:01:12.000Z",
  "title": "Subconvexity for $GL(3)\\times GL(2)$ $L$-functions in $t$-aspect",
  "authors": [
    "Ritabrata Munshi"
  ],
  "comment": "first draft",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $\\pi$ be a Hecke-Maass cusp form for $SL(3,\\mathbb Z)$ and $f$ be a holomorphic (or Maass) Hecke form for $SL(2,\\mathbb{Z})$. In this paper we prove the following subconvex bound $$ L\\left(\\tfrac{1}{2}+it,\\pi\\times f\\right)\\ll_{\\pi,f,\\varepsilon} (1+|t|)^{\\frac{3}{2}-\\frac{1}{42}+\\varepsilon}. $$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-01T06:01:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "subconvexity",
      "hecke-maass cusp form",
      "hecke form",
      "subconvex bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}