{
  "id": "2308.10485",
  "version": "v1",
  "published": "2023-08-21T06:01:09.000Z",
  "updated": "2023-08-21T06:01:09.000Z",
  "title": "Counting elements of the congruence subgroup",
  "authors": [
    "Kamil Bulinski",
    "Igor E. Shparlinski"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We obtain asymptotic formulas for the number of matrices in the congruence subgroup \\[ \\Gamma_0(Q) = \\left\\{ A\\in\\mathrm{SL}_2(\\mathbb Z):~c \\equiv 0 \\pmod Q\\right\\}, \\] which are of naive height at most $X$. Our result is uniform in a very broad range of values $Q$ and $X$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-21T06:01:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "congruence subgroup",
      "counting elements",
      "asymptotic formulas",
      "broad range"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}