{
  "id": "0902.4169",
  "version": "v3",
  "published": "2009-02-24T15:20:53.000Z",
  "updated": "2010-01-13T21:45:00.000Z",
  "title": "Arithmetic theory of q-difference equations (G_q-functions and q-difference modules of type G, global q-Gevrey series)",
  "authors": [
    "Lucia Di Vizio"
  ],
  "comment": "This paper won't be submitted for publication since the results below can be obtained in a more direct way",
  "categories": [
    "math.NT",
    "math.QA"
  ],
  "abstract": "In the first part of the paper we give a definition of G_q-function and we establish a regularity result, obtained as a combination of a q-analogue of the Andre'-Chudnovsky Theorem [And89, VI] and Katz Theorem [Kat70, \\S 13]. In the second part of the paper, we combine it with some formal q-analogous Fourier transformations, obtaining a statement on the irrationality of special values of the formal $q$-Borel transformation of a G_q-function.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2010-01-13T21:45:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "39A13",
      "12H99",
      "33D15",
      "11J72"
    ],
    "keywords": [
      "global q-gevrey series",
      "arithmetic theory",
      "q-difference equations",
      "q-difference modules",
      "formal q-analogous fourier transformations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0902.4169D"
    }
  }
}