Automorphic forms on the upper half plane have been studied for a long time. He extended Hecke’s relation between automorphic forms and Dirichlet series to real analytic automorphic forms.
This book studies the modules arising in Fourier expansions of automorphic forms, namely Fourier term modules on SU(2,1), the smallest rank one Lie group with a non-abelian unipotent subgroup.