{
  "id": "2005.08185",
  "version": "v1",
  "published": "2020-05-17T08:01:41.000Z",
  "updated": "2020-05-17T08:01:41.000Z",
  "title": "A subconvex bound for twisted $L$-functions",
  "authors": [
    "Qingfeng Sun",
    "Hui Wang"
  ],
  "comment": "12 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $\\mathfrak{q}>2$ be a prime number, $\\chi$ a primitive Dirichlet character modulo $\\mathfrak{q}$ and $f$ a primitive holomorphic cusp form or a Hecke-Maass cusp form of level $\\mathfrak{q}$ and trivial nebentypus. We prove the subconvex bound $$ L(1/2,f\\otimes \\chi)\\ll \\mathfrak{q}^{1/2-1/12+\\varepsilon}, $$ where the implicit constant depends only on the archimedean parameter of $f$ and $\\varepsilon$. The main input is a modifying trivial delta method developed in [1].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-17T08:01:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F66"
    ],
    "keywords": [
      "subconvex bound",
      "modifying trivial delta method",
      "primitive holomorphic cusp form",
      "primitive dirichlet character modulo",
      "hecke-maass cusp form"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}