Zeta function of Selberg's type for compact quotient of SU(n,1) (n\(\geq 2)\) (Q802594)

The author studies a generalization of the Selberg zeta function for cocompact discrete subgroups of SU(n,1), \(n\geq 2\). The novel feature here is that the automorphic forms are associated with one-dimensional representations of \(SU(n,1)\cap U(n+1)\). The set of the representations is parametrized by \({\mathbb{Z}}\). By and large the analysis follows the classical lines laid down by Selberg but the analysis of the corresponding spherical functions has several points of interest. He obtains a formula for the multiplicity of a member of the discrete series, and also the analytic properties of the Selberg zeta functions, which are analogous to the usual ones.