Units in families of totally complex algebraic number fields (Q1777703)

In this particularly well written work, the author applies a multidimensional continued fraction algorithm to determine systems of fundamental units in certain families of totally complex algebraic number fields, of degrees four, six and eight. The algorithm is an analog of one given in the author's paper [Trans. Am. Math. Soc. 356, No. 6, 2325--2348 (2004; Zbl 1055.11065)], and here determines the units of interest by way of determining a fundamental domain for the action of \(\text{GL}_n(\mathcal O_K)/\mu_K\) acting on the Hermitian symmetric space \(\text{SL}_n(\mathbb C)/\text{SU}(n)\), where \(\mathcal O_K\) is the ring of integers of the number field at hand, \(\mu_K\) is the group of roots of unity in \(\mathcal O_K\).