{
  "id": "2007.09508",
  "version": "v1",
  "published": "2020-07-18T19:49:33.000Z",
  "updated": "2020-07-18T19:49:33.000Z",
  "title": "Elliptic (p,q)-difference modules",
  "authors": [
    "Ehud de Shalit"
  ],
  "comment": "34 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We study finite dimensional vector spaces over fields of elliptic functions equipped with two commuting aotomorphisms \\sigma and \\tau induced by isogenies of relatively prime orders. We give a structure theorem for such objects, that reveals a connection to the classification of vector bundles on elliptic curves by Atiyah. As an application we prove an elliptic analogue of a conjecture of Loxton and van der Poorten which has been recently proved by Adamczewski and Bell.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-18T19:49:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "39A10",
      "12H10",
      "14H52"
    ],
    "keywords": [
      "study finite dimensional vector spaces",
      "van der poorten",
      "elliptic functions",
      "elliptic analogue",
      "elliptic curves"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}