{
  "id": "1805.04892",
  "version": "v1",
  "published": "2018-05-13T14:15:22.000Z",
  "updated": "2018-05-13T14:15:22.000Z",
  "title": "Subconvexity bound for $GL(2)$ L-functions: \\lowercase{t}-aspect",
  "authors": [
    "Ratnadeep Acharya",
    "Sumit Kumar",
    "Gopal Maiti",
    "Saurabh Kumar Singh"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $f $ be a holomorphic Hecke eigenform or a Hecke-Maass cusp form for the full modular group $ SL(2, \\mathbb{Z})$. In this paper we shall use circle method to prove the Weyl exponent for $GL(2)$ $L$-functions. We shall prove that \\[ L \\left( \\frac{1}{2} + it, f \\right) \\ll_{f, \\epsilon} \\left( 2 + |t|\\right)^{1/3 + \\epsilon}, \\] for any $\\epsilon > 0.$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-13T14:15:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F66",
      "11M41",
      "11F55"
    ],
    "keywords": [
      "subconvexity bound",
      "l-functions",
      "holomorphic hecke eigenform",
      "hecke-maass cusp form",
      "full modular group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}