{
  "id": "2012.10835",
  "version": "v1",
  "published": "2020-12-20T03:28:09.000Z",
  "updated": "2020-12-20T03:28:09.000Z",
  "title": "Bounds for $\\rm GL_2\\times GL_2$ $L$-functions in depth aspect",
  "authors": [
    "Qingfeng Sun"
  ],
  "comment": "15 pages. Comments are welcome!",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $f$ and $g$ be holomorphic or Maass cusp forms for $\\rm SL_2(\\mathbb{Z})$ and let $\\chi$ be a primitive Dirichlet character of prime power conductor $\\mathfrak{q}=p^{\\kappa}$ with $p$ prime and $\\kappa>12$. A subconvex bound for the central values of the Rankin-Selberg $L$-functions $L(s,f\\otimes g \\otimes \\chi)$ is proved in the depth-aspect $$ L\\left(\\frac{1}{2},f\\otimes g \\otimes \\chi\\right)\\ll_{f,g,\\varepsilon} p^{3/4}\\mathfrak{q}^{15/16+\\varepsilon}. $$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-20T03:28:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "depth aspect",
      "maass cusp forms",
      "prime power conductor",
      "primitive dirichlet character",
      "subconvex bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}