On Discriminant Functions Associated to Drinfeld Modules of Rank 1 Original Research Article

Let k be a global function field with constant field imageq. Let ∞ be a place of k and let imagek be the ring of functions regular outside of ∞. Once a sign function has been chosen, one can define a discriminant function on the set of rank 1 Drinfeld imagek-modules. In this paper, the connection between sign functions and discriminant functions is clarified. Moreover, building on previous work of Hayes, some arithmetic properties of exponential functions of rank 1 lattices are also presented.