### Can a Drinfeld module be modular?, by David Goss

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, Gebhard Boeckle attaches
abelian Galois representations to characteristic p valued cusp eigenforms and
double cusp eigenforms 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
Boeckle's paper with an emphasis on modularity and closes with some specific
questions raised by his work.

David Goss <goss@math.ohio-state.edu>