{
  "id": "2203.10025",
  "version": "v1",
  "published": "2022-03-18T15:52:54.000Z",
  "updated": "2022-03-18T15:52:54.000Z",
  "title": "Sharp estimates for the hypergeometric functions related to root systems of type $A$ and of rank 1",
  "authors": [
    "Piotr Graczyk",
    "Patrice Sawyer"
  ],
  "categories": [
    "math.CA",
    "math.RT"
  ],
  "abstract": "In this article, we conjecture exact estimates for the Weyl-invariant Opdam-Cherednik hypergeometric functions. We prove the conjecture for the root system $A_n$ and for all rank 1 cases. We provide other evidence that the conjecture might be true in general.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-18T15:52:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C67",
      "31B05",
      "53C35",
      "33C05"
    ],
    "keywords": [
      "root system",
      "sharp estimates",
      "weyl-invariant opdam-cherednik hypergeometric functions",
      "conjecture exact estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}