{
  "id": "2104.13025",
  "version": "v1",
  "published": "2021-04-27T07:54:26.000Z",
  "updated": "2021-04-27T07:54:26.000Z",
  "title": "Uniform subconvexity bounds for $GL(3) \\times GL(2)$ $L$-functions",
  "authors": [
    "Bingrong Huang"
  ],
  "comment": "31 pages. Comments are welcome!",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, we prove uniform subconvexity bounds for $GL(3)\\times GL(2)$ $L$-functions in the $GL(2)$ spectral aspect and the $t$ aspect via a delta method. More precisely, let $\\phi$ be a Hecke--Maass cusp form for $SL(3,\\mathbb{Z})$ and $f$ a Hecke--Maass cusp form for $SL(2,\\mathbb{Z})$ with the spectral parameter $t_f$. Then for $t\\in\\mathbb{R}$ and any $\\varepsilon>0$, we have \\[ L(1/2+it,\\phi\\times f) \\ll_{\\phi,\\varepsilon} (t_f+|t|)^{27/20+\\varepsilon}. \\] Moreover, we get subconvexity bounds for $L(1/2+it,\\phi\\times f)$ whenever $|t|-t_f \\gg (|t|+t_f)^{3/5+\\varepsilon}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-27T07:54:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "uniform subconvexity bounds",
      "hecke-maass cusp form",
      "spectral aspect",
      "delta method",
      "spectral parameter"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}