{
  "id": "2403.08324",
  "version": "v1",
  "published": "2024-03-13T08:21:13.000Z",
  "updated": "2024-03-13T08:21:13.000Z",
  "title": "Mixed moments of $\\rm GL(2)$ and symmetric square $L$-functions",
  "authors": [
    "Bingrong Huang",
    "Liangxun Li"
  ],
  "comment": "25 pages. Comments welcome!",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, we prove asymptotic formulas of mixed moments of $\\rm GL(2)$ and its symmetric square $L$-functions for both Hecke--Maass cusp forms and holomorphic Hecke eigenforms in short intervals. As an application, we prove quantitative simultaneous non-vanishing of central values of these $L$-functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-13T08:21:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "symmetric square",
      "mixed moments",
      "holomorphic hecke eigenforms",
      "hecke-maass cusp forms",
      "asymptotic formulas"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}