{
  "id": "2303.09646",
  "version": "v1",
  "published": "2023-03-16T20:57:25.000Z",
  "updated": "2023-03-16T20:57:25.000Z",
  "title": "Subconvexity for $GL(1)$ twists of Rankin-Selberg $L$-functions",
  "authors": [
    "Aritra Ghosh"
  ],
  "comment": "First Draft. arXiv admin note: text overlap with arXiv:2111.00696",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $f$ and $g$ be two Hecke-Maass or holomorphic primitive cusp forms for $SL(2,\\mathbb{Z})$ and $\\chi$ be a primitive Dirichlet character of modulus $p$, a prime. A subconvex bound for the central values of the Rankin-Selberg L-functions is $L(s, f \\otimes g \\otimes \\chi)$ is give by $$L(\\frac{1}{2}, f \\otimes g \\otimes \\chi) \\ll_{f,g,\\epsilon} {p}^{1- \\left(\\frac{1-2\\theta}{5+2\\theta}\\right) +\\epsilon} ,$$ for any $\\epsilon > 0$, where the implied constant depends only on the forms $f,g$ and $\\epsilon$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-16T20:57:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "subconvexity",
      "holomorphic primitive cusp forms",
      "primitive dirichlet character",
      "rankin-selberg l-functions",
      "subconvex bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}