摘要
Let F∞=Fq((1/T)) be the completion of F q (T) at 1/T. We develop a theory of Fourier expansions for harmonic cochains on the edges of the Bruhat–Tits building of PGLr(F∞), r≥ 2 , generalizing an earlier construction of Gekeler for r= 2. We then apply this theory to study modular units on the Drinfeld symmetric space Ω r over F ∞ , and the cuspidal divisor groups of Satake compactifications of certain Drinfeld modular varieties. In particular, we obtain a higher dimensional analogue of a result of Ogg for classical modular curves X(p) of prime level.