{
  "id": "1503.05973",
  "version": "v1",
  "published": "2015-03-20T00:33:49.000Z",
  "updated": "2015-03-20T00:33:49.000Z",
  "title": "Sparse Equidistribution of Unipotent Orbits in Finite-Volume Quotients of $\\text{PSL}(2,\\mathbb R)$",
  "authors": [
    "Cheng Zheng"
  ],
  "comment": "18 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "In this note, we consider the orbits $\\{pu(n^{1+\\gamma})|n\\in\\mathbb N\\}$ in $\\Gamma\\backslash\\text{PSL}(2,\\mathbb R)$, where $\\Gamma$ is a non-uniform lattice in $\\text{PSL}(2,\\mathbb R)$ and $u(t)$ is the standard unipotent group in $\\text{PSL}(2,\\mathbb R)$. Under a Diophantine condition on the intial point $p$, we can prove that $\\{pu(n^{1+\\gamma})|n\\in\\mathbb N\\}$ is equidistributed in $\\Gamma\\backslash\\text{PSL}(2,\\mathbb R)$ for small $\\gamma>0$, which generalizes a result of Venkatesh (Ann.of Math. 2010).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-20T00:33:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E40",
      "37A17"
    ],
    "keywords": [
      "unipotent orbits",
      "finite-volume quotients",
      "sparse equidistribution",
      "standard unipotent group",
      "diophantine condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150305973Z"
    }
  }
}