{
  "id": "math/0210388",
  "version": "v2",
  "published": "2002-10-24T16:38:03.000Z",
  "updated": "2003-01-05T21:29:12.000Z",
  "title": "Can a Drinfeld module be modular?",
  "authors": [
    "David Goss"
  ],
  "comment": "Final corrected version",
  "journal": "Journal of the Ramanujan Math. Soc. {\\bf 17} No. 4 (2002) 221-260",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "Let $k$ be a global function field with field of constants $\\Fr$ and let $\\infty$ be a fixed place of $k$. In his habilitation thesis \\cite{boc2}, Gebhard B\\\"ockle attaches abelian Galois representations to characteristic $p$ valued cusp eigenforms and double cusp eigenforms \\cite{go1} such that Hecke eigenvalues correspond to the image of Frobenius elements. In the case where $k=\\Fr(T)$ and $\\infty$ corresponds to the pole of $T$, it then becomes reasonable to ask whether rank 1 Drinfeld modules over $k$ are themselves ``modular'' in that their Galois representations arise from a cusp or double cusp form. This paper gives an introduction to \\cite{boc2} with an emphasis on modularity and closes with some specific questions raised by B\\\"ockle's work.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2003-01-05T21:29:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F52"
    ],
    "keywords": [
      "drinfeld module",
      "cusp eigenforms",
      "attaches abelian galois representations",
      "galois representations arise",
      "hecke eigenvalues correspond"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math.....10388G"
    }
  }
}