2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65425Let $k$ 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 Böckle 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 Böckle's work.Final corrected versionNumber TheoryAlgebraic Geometry11F52text