Simultaneous number systems in the lattice of Eisenstein integers

Abstract. The notion of simultaneous number systems was introduced by Kátai et al. in [1]. In this paper simultaneous number systems constructions are investigated in the lattice of Eisenstein integers. We show that except for \(8\) trivial cases for each Eisenstein integer \(\eta_1\) there is an Eisenstein integer \(\eta_2\) and some appropriate digit set \(D\) such that \((\eta_1,\eta_2,D)\) forms a simultaneous number system.