Parshin, A. N. Note on the Siegel formula. (English. Russian original) Zbl 0999.20040 J. Math. Sci., New York 106, No. 5, 3336-3339 (2001); translation from Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat. Obz. 70, VINITI, Moscow 159-164 (2001). In this short report the author indicates a generalization of the formulae for the covolume of the group \(G(A)\) in \(G(K\otimes\mathbb{R})\) where \(A\) denotes the ring of integers in a totally real algebraic number field \(K\) and \(G\) is a semisimple simply connected algebraic group defined over \(K\). Such formulae are named after C. L. Siegel who proved certain cases for a number of series of \(G\). Here the author regards \(A\) as “being” an arithmetic scheme of dimension 1 and discusses what happens when the dimension is 0 or \(>1\). Reviewer: Samuel James Patterson (Göttingen) Cited in 2 Documents MSC: 20G35 Linear algebraic groups over adèles and other rings and schemes 22E40 Discrete subgroups of Lie groups Keywords:Tamagawa numbers; Siegel formula; zeta functions; covolumes; rings of integers; totally real algebraic number fields; semisimple simply connected algebraic groups; arithmetic schemes PDFBibTeX XMLCite \textit{A. N. Parshin}, J. Math. Sci., New York 106, No. 5, 3336--3339 (2001; Zbl 0999.20040); translation from Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat. Obz. 70, VINITI, Moscow 159--164 (2001) Full Text: DOI