Characterization of quadratic ε−CNS polynomials

Abstract

In this paper, we give characterization of quadratic ε-canonical number system (ε−CNS) polynomials for all values ε∈[0,1). Our characterization provides a unified view of the well-known characterizations of the classical quadratic CNS polynomials (ε=0) and quadratic SCNS polynomials (ε=1/2). This result is a consequence of our new characterization results of ε-shift radix systems (ε−SRS) in the two-dimensional case and their relation to quadratic ε−CNS polynomials.