{
  "id": "1803.00542",
  "version": "v1",
  "published": "2018-03-01T18:23:32.000Z",
  "updated": "2018-03-01T18:23:32.000Z",
  "title": "The Burgess bound via a trivial delta method",
  "authors": [
    "Keshav Aggarwal",
    "Roman Holowinsky",
    "Yongxiao Lin",
    "Qingfeng Sun"
  ],
  "comment": "13 pages; comments welcome",
  "categories": [
    "math.NT"
  ],
  "abstract": "Recently, Munshi established the following Burgess bounds ${L(1/2,g\\otimes \\chi)\\ll_{g,\\varepsilon} M^{1/2-1/8+\\varepsilon}}$ and $L(1/2,\\chi)\\ll_{\\varepsilon} M^{1/4-1/16+\\varepsilon}$, for any given $\\varepsilon>0$, where $g$ is a fixed Hecke cusp form for $\\rm SL(2,\\mathbb{Z})$, and $\\chi$ is a primitive Dirichlet character modulo a prime $M$. The key to his proof was his novel $\\rm GL(2)$ delta method. In this paper, we give a new proof of these Burgess bounds by using a trivial delta method.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-03-01T18:23:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F66"
    ],
    "keywords": [
      "trivial delta method",
      "burgess bound",
      "fixed hecke cusp form",
      "primitive dirichlet character modulo"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}