{
  "id": "math/0610962",
  "version": "v1",
  "published": "2006-10-31T09:36:18.000Z",
  "updated": "2006-10-31T09:36:18.000Z",
  "title": "Generating functions for Hecke operators",
  "authors": [
    "Hala Hajj Shehadeh",
    "Samar Jaafar",
    "Kamal Khuri-Makdisi"
  ],
  "comment": "13 pages",
  "journal": "International Journal of Number Theory 5 (2009), no. 1, 125-140",
  "categories": [
    "math.NT"
  ],
  "abstract": "Fix a prime N, and consider the action of the Hecke operator T_N on the space M_k(SL(2,Z)) of modular forms of full level and varying weight k. The coefficients of the matrix of T_N with respect to the basis {E_4^i E_6^j | 4i + 6j = k} for M_k(SL(2,Z)) can be combined for varying k into a generating function F_N. We show that this generating function is a rational function for all N, and present a systematic method for computing F_N. We carry out the computations for N = 2, 3, 5, and indicate and discuss generalizations to spaces of modular forms of arbitrary level.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-10-31T09:36:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F32",
      "13D40",
      "11F11"
    ],
    "keywords": [
      "generating function",
      "hecke operator",
      "modular forms",
      "arbitrary level",
      "systematic method"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....10962H"
    }
  }
}