Cyclotomic fields are characterized by their trace lattices (Q2192147)

For a \(CM\)-field \(K\) put \(q_K(x,y)=Tr_{K/\mathbb Q}(x\bar y)\), \(\bar y\) denoting the complex conjugate of \(y\), and let \((Z_K,q_K)\) denote the lattice formed by the restriction of \(q_K\) to the ring \(Z_K\) of integers of \(K\). The author shows that is \(L\) is a cyclotomic field and the lattices \((Z_K,q_K)\) and \((Z_L,q_L)\) are isomorphic, then the fields \(K, L\) are isomorphic. It is shown by an example that this assertion does not hold for a pair of arbitrary \(CM\)-fields.