Hoffmann, Werner The non-semi-simple term in the trace formula for rank one lattices. (English) Zbl 0609.22005 J. Reine Angew. Math. 379, 1-21 (1987). A problem in the derivation of the Selberg trace formula for rank one lattices \(\Gamma\) in real reductive Lie groups \(G\) is solved. The representation \(L^{dis}\) of \(G\) by left translations in the maximal completely reducible subspace of \(L^ 2(G/\Gamma)\) extends to the algebra of smooth compactly supported functions \(\alpha\) on \(G\). The point is to express \(trace(L^{dis}(\alpha))\) by familiar distributions. It is shown how the contribution of the non-semi-simple elements of \(\Gamma\) to this trace can be expressed by weighted orbital integrals, which was previously known in general only for the semi-simple elements. Cited in 5 Documents MSC: 22E40 Discrete subgroups of Lie groups 22E35 Analysis on \(p\)-adic Lie groups 11F72 Spectral theory; trace formulas (e.g., that of Selberg) 43A85 Harmonic analysis on homogeneous spaces 43A15 \(L^p\)-spaces and other function spaces on groups, semigroups, etc. Keywords:Selberg trace formula; rank one lattices; real reductive Lie groups; distributions; weighted orbital integrals PDFBibTeX XMLCite \textit{W. Hoffmann}, J. Reine Angew. Math. 379, 1--21 (1987; Zbl 0609.22005) Full Text: DOI Crelle EuDML