{
  "id": "2112.14562",
  "version": "v2",
  "published": "2021-12-29T14:11:07.000Z",
  "updated": "2022-06-03T20:47:28.000Z",
  "title": "Polynomial effective density in quotients of $\\mathbb H^3$ and $\\mathbb H^2\\times\\mathbb H^2$",
  "authors": [
    "Elon Lindenstrauss",
    "Amir Mohammadi"
  ],
  "comment": "76 pages",
  "categories": [
    "math.DS",
    "math.GT",
    "math.MG"
  ],
  "abstract": "We prove effective density theorems, with a polynomial error rate, for orbits of the upper triangular subgroup of $\\operatorname{SL}_2(\\mathbb R)$ in arithmetic quotients of $\\operatorname{SL}_2(\\mathbb C)$ and $\\operatorname{SL}_2(\\mathbb R)\\times\\operatorname{SL}_2(\\mathbb R)$. The proof is based on the use of a Margulis function, tools from incidence geometry, and the spectral gap of the ambient space.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-06-03T20:47:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "polynomial effective density",
      "polynomial error rate",
      "upper triangular subgroup",
      "ambient space",
      "effective density theorems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 76,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}