Some results on simultaneous number systems
in the ring of integers of imaginary quadratic fields

Abstract. Simultaneous number systems were analysed in the ring of the Gaussian and the Eisenstein integers in [5, 3, 7,8] In this paper we present some results for further characterisations in the rings of integers of general imaginary quadratic fields. We show that in each ring there are infinitely many simultaneous number systems, and we give an efficient algorithm for the decision problem.