Isogenous tori and the class number formulae (Q1191307)

First, the author gives the detailed proofs of the results announced in his previous papers [Proc. Japan Acad., Ser. A 62, 216--218 (1986; Zbl 0613.12004), ibid. 62, 320--322 (1986; Zbl 0613.12005)], in which he generalized the result of \textit{T. Ono} [Nagoya Math. J. 107, 121--133 (1987; Zbl 0642.12018)]. Next, he generalizes the Dirichlet class number relation for bicyclic biquadratic extension \(K/F\), using purely algebraic methods. As a corollary of this formula, he obtains the well known class number formula for \(\mathbb Q(\sqrt q,\sqrt {-1})\), where \(q\) is prime.