Rotated \(D_n\)-lattices (Q452375)

The paper gives explicit examples of lattices isometric to the \(D_n\)-lattices in the maximal real subfields of the cyclotomic fields \(K = {\mathbb Q}(\zeta _m +\zeta_m^{-1})\) for \(m\) a prime or a power of \(2\). Using the real embeddings of \(K\) these lattices are identified as sublattices of \({\mathbb R}^n\) and their minimum product distance is computed.