Zeta functions of Selberg’s type for some noncompact quotients of symmetric spaces of rank one

Source abstract

In a previous paper [5], one of the present authors has worked out a theory of zeta functions of Selberg’s type for compact quotients of symmetric spaces of rank one. In the present paper, we consider the analogues of those results when G/K is a noncompact symmetric space of rank one and Γ is a discrete subgroup of G such that G/Γ is not compact but such that vol( G/Γ )<∞. Thus, Γ is a non-uniform lattice. Certain mild restrictions, which are fulfilled in many arithmetic cases, will be put on Γ , and we shall consider how one can define a zeta function Z Γ of Selberg’s type attached to the data ( G, K, Γ ).