{
  "id": "2408.14046",
  "version": "v1",
  "published": "2024-08-26T07:00:52.000Z",
  "updated": "2024-08-26T07:00:52.000Z",
  "title": "The Divisibility of $\\mathrm{GL}(n, q)$ Character Values",
  "authors": [
    "Varun Shah",
    "Steven Stallone"
  ],
  "comment": "20 pages",
  "categories": [
    "math.RT",
    "math.CO"
  ],
  "abstract": "Let $q$ be a prime power, and $d$ a positive integer. We study the proportion of irreducible characters of $\\mathrm{GL}(n,q)$ whose values evaluated on a fixed matrix $g$ are divisible by $d$. As $n$ approaches infinity, this proportion tends to $1$ when $q$ is coprime to $d$. When $q$ and $d$ are not coprime, and $g=1$, this proportion is bounded above by $\\frac{1}{q}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-26T07:00:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "character values",
      "divisibility",
      "prime power",
      "proportion tends"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}