On the growth of the number of primitive totally geodesic surfaces in some hyperbolic 3-manifolds

Abstract

Let d be a positive square-free integer ≡3(mod4) such that the ideal class group of Q[−d] does not contain an element of order 4. We prove an asymptotic formula for the number of primitive immersed totally geodesic surfaces in Γ−d\\H3 having area less than X.