On some class number relations for Galois extensions (Q5903005)

Let \(K\) be a finite Galois extension of an algebraic number field k. The algebraic torus T is defined to be the kernel of the norm map \(R_{K/k}(G_ m/k)\to G_ m/k\). Let \(h_ K\), \(h_ k\), \(h_{K/k}\) be the class numbers of K, k, T, respectively. Let E(K/k) be \(h_ K (h_ k h_{K/k})^{-1}\). The author reports a formula for E(K/k) correcting a previously announced formula for cyclic Kummer extensions [ibid. 61, 109- 111 (1985; Zbl 0578.12003)].