{
  "id": "1202.4068",
  "version": "v1",
  "published": "2012-02-18T10:42:24.000Z",
  "updated": "2012-02-18T10:42:24.000Z",
  "title": "The circle method and bounds for $L$-functions - I",
  "authors": [
    "Ritabrata Munshi"
  ],
  "comment": "8 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $f$ be a Hecke-Maass or holomorphic primitive cusp form of arbitrary level and nebentypus, and let $\\chi$ be a primitive character of conductor $M$. For the twisted $L$-function $L(s,f\\otimes \\chi)$ we establish the hybrid subconvex bound $$ L(1/2+it,f\\otimes\\chi)\\ll (M(3+|t|))^{1/2-1/18+\\varepsilon}, $$ for $t\\in \\mathbb R$. The implied constant depends only on the form $f$ and $\\varepsilon$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-02-18T10:42:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "circle method",
      "holomorphic primitive cusp form",
      "hybrid subconvex bound",
      "arbitrary level",
      "implied constant depends"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1202.4068M"
    }
  }
}