Abstract.
We consider the Hecke groups generated by \( S(z)=z+\lambda \) and \( T(z)=-1/z \) with \( \lambda=2\cos(\pi/q) \) for \( q\geqq 3 \). We show that when \( q=4 \) or 6, the units in \( \mathbb{Z}[\lambda] \) are infinite pure periodic \( \lambda \)-fractions, and hence cannot be cusp points (images of \( \infty \) by a member of the group.) The case when \( q=7 \) is quite different; examples of units that are finite \( \lambda \)-fractions and units that are infinite \( \lambda \)-fractions are given. We conclude with a conjecture on the structure of these infinite repeating units.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Eingegangen am 3.2.2000
Rights and permissions
About this article
Cite this article
Rosen, D., Towse, C. Continued fraction representations of units associated with certain Hecke groups. Arch. Math. 77, 294–302 (2001). https://doi.org/10.1007/PL00000494
Issue Date:
DOI: https://doi.org/10.1007/PL00000494