The distribution of reduced numbers in an ideal of a real cubic number field
According to the abstract of the author: ''Let K be a real but not totally real field of degree three over \({\mathbb{Q}}\), and let A be an ideal in K. It is proved that the reduced numbers in A (i.e., numbers \(\alpha\) with \(\alpha >1\) and \(-1<Re \alpha^{(j)}<0\) for all conjugates \(\alpha^{(j)}\neq \alpha)\) are dense in a set of intervals of constant length, and no reduced numbers in A occur in the gaps between these intervals. In fact, the intervals are determined explicitly, and criteria are given for when the reduced numbers in A actually are dense in the whole of \([1,\infty).\)''
scientific article; zbMATH DE number 3904699