{
  "annotation_id": "dcafd1fb-ad58-48d3-a1f8-8e02cd7b3c67",
  "date_created": "2026-02-17T05:53:24.226000Z",
  "date_modified": "2026-02-17T05:53:24.226000Z",
  "file_hash": "1a6e20135eafc08ccbeb62d986c08438e2ba0fb4690ad1c2b2676ed43ce6607c",
  "private": false,
  "record": {
    "abstract": "We sketch the proof of an effective equidistribution theorem for one-parameter unipotent subgroups in $S$-arithmetic quotients arising from $\\mathbf K$-forms of $\\mathrm{SL}_2^{\\mathsf n}$ where $\\mathbf K$ is a number field. This gives an effective version of equidistribution results of Ratner and Shah with a polynomial rate.\n  The key new phenomenon is the existence of many intermediate groups between the $\\mathrm{SL}_2$ containing our unipotent and the ambient group, which introduces potential local and global obstruction to equidistribution.\n  Our approach relies on a Bourgain-type projection theorem in the presence of obstructions, together with a careful analysis of these obstructions.",
    "arxiv_id": "2601.09983",
    "authors": [
      "Elon Lindenstrauss",
      "Amir Mohammadi",
      "Lei Yang"
    ],
    "categories": [
      "math.DS",
      "math.CA",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Polynomially effective equidistribution for unipotent orbits in products of $\\mathrm{SL}_2$ factors",
    "url": "https://arxiv.org/abs/2601.09983",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "1dc2c663-2f5e-4160-a963-8a71ed3dd2da",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}