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 <>