Über die Spitzenbreiten von Kongruenzuntergruppen der rationalen Modulgruppe. (On the cusp amplitudes of congruence subgroups of the rational modular group)
type: Item
instance of: scholarly article
title: Über die Spitzenbreiten von Kongruenzuntergruppen der rationalen Modulgruppe. (On the cusp amplitudes of congruence subgroups of the rational modular group)
zbMATH Open document ID: 0707.11031
DOI: 10.1007/BF02942319
published in: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
publication date: 1989-01-01T00:00:00Z
review text: In a previous paper it was shown by the author that the level of a congruence subgroup of the classical modular group always equals the least common multiple (lcm) of all the cusp amplitudes. Stemming on a finer result of \textit{H. Larcher} [Ill. J. Math. 26, 164-172 (1982; Zbl 0467.20039)] the author proves by elementary number-theoretic arguments that for a congruence subgroup with cusps \(\infty,0,1\) the level is already given by the lcm of the amplitudes of the cusps. Furthermore he characterizes those numbers e,f,g to be amplitudes of cusps \(\infty,0,1\) respectively and determines all the amplitudes h of the group \(\Gamma(e,f,g)\), more precisely: \(\gcd(e,f,g) | h | lcm(e,f,g)\).
Mathematics Subject Classification ID: 11F06
Mathematics Subject Classification ID: 20H05
zbMATH DE Number: 4160840
zbMATH Keywords: level
zbMATH Keywords: congruence subgroup of the classical modular group
zbMATH Keywords: cusp amplitudes
author: Klaus Wohlfahrt
MaRDI profile type: Publication
cites work: The cusp amplitudes of the congruence subgroups of the classical modular group
cites work: An extension of F. Klein's level concept
full work available at URL: https://doi.org/10.1007/bf02942319
OpenAlex ID: W2078333108
description: scientific article; zbMATH DE number 4160840