Drinfeld discriminant function and Fourier expansion of harmonic cochains

Contact: Pieter Moree (moree @ mpim-bonn.mpg.de)

We study the relationship between the modular units on the Drinfeld symmetric space, the harmonic cochains on the edges of the Bruhat-Tits building of PGL(r), and the cuspidal divisor groups of certain Drinfeld modular varieties of dimension r-1, where r is an arbitrary integer >1. As an application, we obtained a higher dimensional analogue of a result of Ogg about the structure of the cuspidal divisor group of the  classical modular curve X_0(p) of prime level. This is joint work with Fu-Tsun Wei.