{
  "id": "2108.03985",
  "version": "v1",
  "published": "2021-08-09T12:37:26.000Z",
  "updated": "2021-08-09T12:37:26.000Z",
  "title": "Simultaneous non-vanishing of central values of $GL(2) \\times GL(3) $ and $GL(3)$ $L$-functions",
  "authors": [
    "Gopal Maiti",
    "Kummari Mallesham"
  ],
  "comment": "Comments are welcome!",
  "categories": [
    "math.NT"
  ],
  "abstract": "We study simultaneous non-vanishing of $L(\\tfrac{1}{2},\\di)$ and $L(\\tfrac{1}{2},g\\otimes \\di)$, when $\\di$ runs over an orthogonal basis of the space of Hecke-Maass cusp forms for $SL(3,\\mathbb{Z})$ and $g$ is a fixed $SL(2,\\mathbb{Z})$ Hecke cusp form of weight $k\\equiv 0 \\pmod 4$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-09T12:37:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "central values",
      "simultaneous non-vanishing",
      "hecke cusp form",
      "hecke-maass cusp forms",
      "orthogonal basis"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}