On the Ore-Krasner equation (Q2842084)

Let \(K\) be a finite extension of \(\mathbb Q_p\), the field of \(p\)-adic numbers. \textit{M. Krasner} [Mathematica, Cluj 13, 72--191 (1937; JFM 63.0880.01)] defined an equivalence relation between the Eisenstein polynomials of degree \(p\) generating cyclic extensions over \(K\). He also proved the existence of privileged representative of each equivalence class which he called ''Reduite''. In the paper under review are determined explicitly the Eisenstein polynomials and their Reduites, in the cyclic case of degree \(p\). The author also provides several numerical examples of Eisenstein polynomials and their Reduites for small primes.