ABSTRACT
In this chapter, the author considers a general survey of the theory of regular and dually regular chains as a convenient tool to treat several number theoretic problems for complex numbers, the real analogs of which are usually treated by means of regular continued fractions. However, in 1975 the author could present the much better theory of regular and dually regular chains in the Gaussian case, hich among other things led to a complete determination of the discrete part of the Gaussian Markoff and Huritz spectra, the result being strikingly similar to Markoff's and Hurwitz' classical theory. The author mentions that a young American mathematician, Norman Richert, has treated the entire subject very thoroughly in his thesis. In particular he has written several BASIC computer programs associated with different aspects of the theory.
