{
  "id": "1312.0553",
  "version": "v1",
  "published": "2013-12-02T19:18:01.000Z",
  "updated": "2013-12-02T19:18:01.000Z",
  "title": "Shifted convolution sums and Burgess type subconvexity over number fields",
  "authors": [
    "P. Maga"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $F$ be a number field and $\\pi$ an irreducible cuspidal representation of $\\mathrm{GL}_{2}(F)\\backslash\\mathrm{GL}_{2}(\\mathbf{A})$ with unitary central character. Then the bound $$L(1/2,\\pi\\otimes\\chi)\\ll_{F,\\pi,\\chi_{\\infty},\\varepsilon} \\mathcal{N}(\\frak{q})^{3/8+\\theta/4+\\varepsilon}$$ holds for any Hecke character $\\chi$ of conductor $\\frak{q}$, where $\\theta$ is any constant towards the Ramanujan-Petersson conjecture ($\\theta=7/64$ is admissible). The proof is based on a spectral decomposition of shifted convolution sums.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-12-02T19:18:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F41",
      "11F70",
      "11M41"
    ],
    "keywords": [
      "shifted convolution sums",
      "burgess type subconvexity",
      "number field",
      "unitary central character",
      "irreducible cuspidal representation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.0553M"
    }
  }
}