Regular chains for equivalent complex irrationals (Q1082363)

In several important papers by \textit{A. L. Schmidt} [Math. Scand. 21(1967), 241-295 (1969; Zbl 0172.066) and Acta Math. 134, 1-85 (1975; Zbl 0329.10023)] the approximation of reals by continued fractions is generalized to the approximation of complex irrationals by Gaussian rationals. The most important tools are unimodular transformations (written as elements from GL(2; \({\mathbb{Z}}[i])\) with determinant \(\pm i\), \(\pm 1)\), regular chains and so called Farey-sets. In the paper under review the author completes a theorem on the characterization of properly equivalent irrational numbers in terms of their regular chains, using some transformations that had not been studied yet.