Knopp, Marvin I.; Newman, Morris On groups related to the Hecke groups. (English) Zbl 0782.11013 Proc. Am. Math. Soc. 119, No. 1, 77-80 (1993). Seien \(A=({1\atop 0} {\lambda_ 1 \atop 1})\), \(B=({1\atop \lambda_ 2} {0\atop 1})\) mit \(\lambda_ 1,\lambda_ 2\in\mathbb{R}\); \(\lambda_ 1,\lambda_ 2>0\); betrachtet als zwei parabolische Elemente der \(\text{PSL}(2,\mathbb{R})\) und \(K(\lambda_ 1,\lambda_ 2)\) die von \(A\) und \(B\) erzeugte Gruppe. \(K(\lambda_ 1,\lambda_ 2)\) ist genau dann diskret, wenn \(\lambda_ 1\lambda_ 2\geq 4\) oder \(\lambda_ 1\lambda_ 2=4\cos^ 2(\pi/p)\), wobei \(p\in\mathbb{N}\), \(p\geq 3\). Reviewer: G.Rosenberger (Dortmund) Cited in 1 Document MSC: 11F06 Structure of modular groups and generalizations; arithmetic groups 20H10 Fuchsian groups and their generalizations (group-theoretic aspects) Keywords:Hecke groups; discrete groups PDFBibTeX XMLCite \textit{M. I. Knopp} and \textit{M. Newman}, Proc. Am. Math. Soc. 119, No. 1, 77--80 (1993; Zbl 0782.11013) Full Text: DOI References: [1] S. Bochner, Some properties of modular relations, Ann. of Math. (2) 53 (1951), 332 – 363. · Zbl 0042.32101 · doi:10.2307/1969546 [2] K. Chandrasekharan and Raghavan Narasimhan, Hecke’s functional equation and arithmetical identities, Ann. of Math. (2) 74 (1961), 1 – 23. · Zbl 0107.03702 · doi:10.2307/1970304 [3] M. I. Knopp, Results related to Hamburger’s theorem (in preparation). [4] Carl Siegel, Bemerkung zu einem Satz von Hamburger über die Funktionalgleichung der Riemannschen Zetafunktion, Math. Ann. 86 (1922), no. 3-4, 276 – 279 (German). · JFM 48.1216.01 · doi:10.1007/BF01457989 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.