An invariant trace formula for the universal covering group of \(\text{SL}(2,\mathbb{R})\)
The fundamental group of \(\text{SL} (2, \mathbb{R})\) is \(\mathbb{Z}\), so that the group possesses a universal cover which is a \(\mathbb{Z}\)-cover. The purpose of the author in this paper is to give the fullest form of the Selberg trace formula (i.e. for Hecke operators) for discrete groups of finite covolume in this universal cover. It turns out that the projection in \(\text{SL} (2, \mathbb{R})\) is again discrete and of finite covolume so that in fact one is dealing with automorphic forms of nonintegral weight for Fuchsian groups of finite covolume (see \S 3 of this paper). The author develops the representation theory and the harmonic analysis in the framework of the universal covering and applies these to prove the versions of the trace formula appropriate to this situation.
scientific article; zbMATH DE number 762849
scientific article