Automorphism polynomials in cyclic cubic extensions (Q1352637)

The author first describes cyclic sextic extensions \(K/k\) with \(k\) being a field of characteristic \(\neq3\) under the assumption that \(\zeta_3\), the cubic root of unity, is contained in \(K\) but not in \(k\), and then determines the minimal polynomial of a generator of \(K/k\) and the generating automorphism of the Galois group. This permits the elimination of the use of computers in the proofs of the main results of \textit{P. Morton} [J. Number Theory 49, 183-208 (1994; Zbl 0810.12003)]. The case when \(k\) is either of characteristic 3 or contains \(\zeta_3\) is treated briefly at the end of the paper.