On existence of canonical number system in certain classes of pure algebraic number fields
The authors consider the existence of canonical number systems or equivalently monogenity of algebraic number fields. They prove that a canonical number system exists in a pure algebraic number field \(L=Q(\vartheta)\), where \(\vartheta\) is a root of the polynomial \(f(x)=x^{2^n}-m\), with a square free integer \(m\not = \pm 1\) and \(m\equiv 2,3\pmod 4\). Moreover, if \(L=Q(\vartheta)\), where \(\vartheta=\root n \of {m}\), with a square-free integer \(m\neq \pm 1\) and all prime factors of \(n\) divide \(m\), then \(L\) is monogenic and the minimal polynomial of \(\vartheta\) is a CNS polynomial.NEWLINENEWLINEThese important results will certainly have many application.
scientific article; zbMATH DE number 6063551