{
  "id": "2001.03186",
  "version": "v1",
  "published": "2020-01-09T19:06:58.000Z",
  "updated": "2020-01-09T19:06:58.000Z",
  "title": "Automorphic $\\mathrm{SL}_2$-periods and the subconvexity problem for $\\mathrm{GL}_2 \\times \\mathrm{GL}_3$",
  "authors": [
    "Aprameyo Pal",
    "Carlos de Vera-Piquero"
  ],
  "comment": "34 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We prove a new (conditional) result towards the subconvexity problem for certain automorphic $L$-functions for $\\mathrm{GL}_2 \\times \\mathrm{GL}_3$. This follows from the computation of new $\\mathrm{SL}_2$-period integrals associated with newforms $f$ and $g$ of even weight and odd squarefree level. The same computations also lead to a central value formula for degree $6$ complex $L$-series of the form $L(f \\otimes \\mathrm{Ad}(g), s)$, extending previous work in arXiv:1804.02352.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-09T19:06:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F67",
      "11F37",
      "11F27"
    ],
    "keywords": [
      "subconvexity problem",
      "automorphic",
      "odd squarefree level",
      "central value formula",
      "computation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}