Cusps of minimal non-compact arithmetic hyperbolic 3-orbifolds

Abstract. In this paper we count the number of cusps of minimal non-compact finite volume arithmetic hyperbolic 3-orbifolds. We show that for each N, the orbifolds of this kind which have exactly N cusps lie in a finite set of commensurability classes, but either an empty or an infinite number of isometry classes. 1. Introduction. In this paper we count the number of cusps of minimal non-compact finite volume arithmetic hyperbolic 3-orbifolds. An orbifold of this kind is isometric to H3/Γ, where H3 is hyperbolic upper half space and Γ is a maximal discrete arithmetic subgroup in PGL2(k) for some imaginary quadratic field k