Trace formulae and applications to class numbers

Abstract

Abstract:In this paper we compute the trace formula for Hecke operators acting on automorphic forms on the hyperbolic 3-space for the group PSL 2 (O K ) with O K being the ring of integers of an imaginary quadratic number field K of class number H K > 1. Furthermore, as a corollary we obtain an asymptotic result for class numbers of binary quadratic forms. MSC:11F25, 11F72

A prime geodesic theorem for higher rank buildings

“…In [8] we applied the Prime Geodesic Theorem for graphs to get class number asymptotics for orders over imaginary quadratic fields. See [14] for a different approach to this case. In the current paper we derive the Prime Geodesic Theorem for quotients of buildings and we use it for class number asymptotics for global fields of characteristic zero.…”