The connections between continued fraction representations of units and certain Hecke groups. (Q974317)

The authors deal with the Hecke groups \(H(\lambda)\) generated by the transformations \(R(z)=\frac{-1}{z}\) and \(T(z)=z+\lambda\), where \(\lambda=\sqrt D\) and \(D\) is a squarefree integer such that \(D=m^2+1\) for \(m=1,3,4,5,\dots\) or \(D=n^2-1\) for \(n=2,3,4,5,\dots\). They prove that the units in \(H(\lambda)\) are infinite pure periodic \(\lambda\)-continued fractions and hence can not be cusp points.