On Demjanenkoʹs Matrix and Mailletʹs Determinant for Imaginary Abelian Number Fields Original Research Article

We construct a generalization of Demjanenkoʹs matrix for an arbitrary imaginary abelian field and prove a relation formula between the determinant of this matrix and the relative class number. In a special case, we prove that the determinant of this matrix coincides with Mailletʹs determinant. As an application, we give an upper bound for the relative class number of any imaginary subfield ofQ(ζ2m).