{
  "id": "1005.2946",
  "version": "v1",
  "published": "2010-05-17T14:59:42.000Z",
  "updated": "2010-05-17T14:59:42.000Z",
  "title": "The action of Hecke operators on hypergeometric functions",
  "authors": [
    "Victor H. Moll",
    "Sinai Robins",
    "Kirk Soodhalter"
  ],
  "comment": "23 pages",
  "categories": [
    "math.NT",
    "math.CA"
  ],
  "abstract": "We study the action of the Hecke operators Un on the set of hy- pergeometric functions, as well as on formal power series. We show that the spectrum of these operators on the set of hypergeometric functions is the set n^a with a an integer and n a positive integer, and that the polylogarithms play a dominant role in the study of the eigenfunctions of the Hecke operators Un on the set of hypergeometric functions. As a corollary of our results on simultaneous eigen- functions, we also obtain an apriori unrelated result regarding the behavior of completely multiplicative hypergeometric coefficients.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-05-17T14:59:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F25",
      "33C05"
    ],
    "keywords": [
      "hypergeometric functions",
      "hecke operators",
      "formal power series",
      "polylogarithms play",
      "dominant role"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1005.2946M"
    }
  }
}