Number expansions over imaginary quadratic Euclidean domains

Abstract

In this dissertation I will define and analyze a number system over norm-Euclidean domains (ENS), and I will generalize the shift radix systems to finite dimensional Hermitian vector spaces (ESRS) using a similar structure. One of the main features of this construction is that the remainder set is the subset of the opened unit disc, which gives us the property that |r| < 1 for every reminder r.