{
  "id": "2410.20569",
  "version": "v1",
  "published": "2024-10-27T19:45:25.000Z",
  "updated": "2024-10-27T19:45:25.000Z",
  "title": "Kloosterman sums on orthogonal groups",
  "authors": [
    "Catinca Mujdei"
  ],
  "comment": "29 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We study Kloosterman sums on the orthogonal groups $SO_{3,3}$ and $SO_{4,2}$, associated to short elements of their respective Weyl groups. An explicit description for these sums is obtained in terms of multi-dimensional exponential sums. These are bounded by a combination of methods from algebraic geometry and $p$-adic analysis.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-27T19:45:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11L05",
      "11L07"
    ],
    "keywords": [
      "orthogonal groups",
      "study kloosterman sums",
      "multi-dimensional exponential sums",
      "adic analysis",
      "explicit description"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}