{
  "id": "2202.11815",
  "version": "v1",
  "published": "2022-02-23T22:35:59.000Z",
  "updated": "2022-02-23T22:35:59.000Z",
  "title": "Polynomial effective equidistribution",
  "authors": [
    "Elon Lindenstrauss",
    "Amir Mohammadi",
    "Zhiren Wang"
  ],
  "comment": "16 pages",
  "categories": [
    "math.DS",
    "math.GT",
    "math.NT"
  ],
  "abstract": "We prove effective equidistribution theorems, with polynomial error rate, for orbits of the unipotent subgroups 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": "v1",
      "updated": "2022-02-23T22:35:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "polynomial effective equidistribution",
      "polynomial error rate",
      "unipotent subgroups",
      "effective equidistribution theorems",
      "arithmetic quotients"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}