The generalized Whittaker functions for $SU(2,1)$ and the Fourier expansion of automorphic forms

Abstract

Explicit form of Fourier expansion of automorphic forms plays an important role in the theory. Here we investigate the case of $SU(2,1)$ and give an explicit formula of generalized Whittaker functions for the standard representations of the group. Togather with a result of [2], we obtain a form of fully developed Fourier expansion of automorphic forms belonging to arbitrary standard representations.