Geometry of biquadratic and cyclic cubic log-unit lattices (Q2043488)

Given a biquadratic or cyclic cubic number field, the authors investigate the lattices formed by the log-embedding of the units of the ring of integers. Among others they determine in the biquadratic case when these (rank 3)-lattices are orthogonal, provide bounds for the size of their fundamental domains and covering radii, and in the cyclic cubic case they show that the lattice is always equilateral triangular, i.e., it has a basis such that the triangle formed by the two basis vectors and the origin is regular.