Hybrid trace formula for a non-uniform irreducible lattice in PSL2(R)n

In a series of lectures Selberg introduced a trace formula on the space of hybrid Maass-modular forms of an irreducible uniform lattice in PSL2(R)n. In this paper we derive the analogous formula for a non-uniform lattice and use it to study the distribution of elliptic–hyperbolic conjugacy classes. In particular, for Hilbert modular groups there is a nice interpretation of these results in terms of class numbers and fundamental units of quadratic forms over totally real number fields.