Whittaker Functions for the Large Discrete Series Representations of $SU(2,1)$ and Related Zeta Integrals

Abstract

In terms of classical Bessel function, we represent explicitly the radial part of Whittaker functions on $SU(2,1)$ belonging to the large discrete series representations. Moreover we compute archimedean local $L$-factors corresponding to a construction of $L$-function by Gelbart and Piatetski–Shapiro.