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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. Together with a result of (K-O), we obtain a form of fully developed Fourier expansion of automorphic forms belonging to arbitrary standard representations.

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