Generalized number systems in Euclidean spaces (Q596988)

The paper surveys mainly known results on number systems in the \(k\)-dimensional Euclidean space \(\mathbb{R}_k\), with \(\mathbb{Z}_k\) the ring of integer vectorials therein. The subgroup \({L}=M\mathbb{Z}_k\) is studied, where \(M\) denotes a \(k\times k\) matrix with integer entries. A digit set is defined in terms of the residue classes \(\pmod L\). In addition, \(q\)-additive and \(q\)-multiplicative functions are studied over the ring of Gaussian integers.