{
  "id": "2211.03030",
  "version": "v1",
  "published": "2022-11-06T05:26:51.000Z",
  "updated": "2022-11-06T05:26:51.000Z",
  "title": "Linear independence of values of the $q$-exponential and related functions",
  "authors": [
    "Anup B. Dixit",
    "Veekesh Kumar",
    "Siddhi S. Pathak"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, we derive results concerning the linear independence of values of the $q$-exponential and certain cognate functions at algebraic arguments when the associated modulus $q$ is a Pisot-Vijayraghavan number. As a consequence, we deduce the irrationality of special values of these functions, some of which were known earlier using alternate methods.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-06T05:26:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11J72",
      "11J87"
    ],
    "keywords": [
      "linear independence",
      "related functions",
      "exponential",
      "algebraic arguments",
      "alternate methods"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}