Trace formulae and applications to class numbers

Abstract

In this paper we compute the trace formula for Hecke operators acting on automorphic forms on the hyperbolic 3-space for the group PSL2($\mathcal{O}_K $) with $\mathcal{O}_K $ being the ring of integers of an imaginary quadratic number field K of class number HK > 1. Furthermore, as a corollary we obtain an asymptotic result for class numbers of binary quadratic forms.