Bases of \(\varepsilon\)-canonical number systems in quadratic number fields (Q6566720)

The paper under review mainly provides an explicit characterization of all bases of \(\varepsilon\)-canonical number system (\(\varepsilon\)-CNS) with finiteness property in the ring of integers \(\mathcal O_L\) of all quadratic number fields \(L=\mathbb Q(\sqrt{D})\) for each \(\varepsilon\in [0,1)\). The main tool is the recent result of \textit{B. Jadrijević} and \textit{K. Miletić} on the characterization of quadratic \(\varepsilon\)-CNS polynomials [J. Number Theory 262, 579--606 (2024; Zbl 1542.11013)].