Generalized number systems in Euclidean spaces
The concept of number systems in higher-dimensional Euclidean spaces as well as in number fields are introduced and treated. The paper is mainly a survey of known results. If Z(k) denotes the ring of integer vectorials in Euclidean space R(k) then we study the subgroup L = MZ(k), where M is a k x k matrix with integer entries. A digit set is defined with the help of residue classes (mod L) A(j) (j = 0,..., t - 1), where t = \det M\. The analogous of q-additive and q-multiplicative functions over the ring of Gaussian integers are also given. (C) 2003 Elsevier Ltd. All rights reserved.
number systems number fields q-additive functions