{
  "id": "1805.02071",
  "version": "v1",
  "published": "2018-05-05T15:42:09.000Z",
  "updated": "2018-05-05T15:42:09.000Z",
  "title": "Central Values of $GL(2)\\times GL(3)$ Rankin-Selberg $L$-functions with Applications",
  "authors": [
    "Qinghua Pi"
  ],
  "comment": "18 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $f$ be a normalized holomorphic cusp form for $SL_2(\\mathbb{Z})$ of weight $k$ with $k\\equiv0\\bmod 4$. By the Kuznetsov trace formula for $GL_3(\\mathbb R)$, we obtain the first moment of central values of $L(s,f\\otimes \\phi)$, where $\\phi$ varies over Hecke-Maass cusp forms for $SL_3(\\mathbb Z)$. As an application, we obtain a non-vanishing result for $L(1/2,f\\otimes\\phi)$ and show that such $f$ is determined by $\\{L(1/2,f\\otimes\\phi)\\}$ as $\\phi$ varies.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-05T15:42:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F11",
      "11F67"
    ],
    "keywords": [
      "central values",
      "application",
      "rankin-selberg",
      "normalized holomorphic cusp form",
      "kuznetsov trace formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}