Inkeri's determinant for an imaginary abelian number field (Q1849630)

Let \(K\) be an imaginary abelian field, \(h_K^-\) the relative class number of \(K\). In his previous paper [Acta Arith. 83, 391-397 (1998; Zbl 0895.11045)], the author gives a formula for \(h_K^-\) in the form of a determinant, which generalizes both formulae for Maillet and Demyanenko determinants. In the present paper, using basic row and column operations, the author modifies the matrix in his formula to obtain a new matrix so that this modified formula can be understood as a generalization of a formula of \textit{K. Inkeri} [Ann. Acad. Sci. Fenn., Ser. A I 199, 1-12 (1955; Zbl 0065.26903)].