Characters and decomposition of a representation in a number field (Q790170)

The author decomposes a representation of the group \((R/I)^*\) (where \(R\) is the ring of integers in an algebraic number field and \(I\) an ideal in \(R\)) on the space of functions on \(R/I\), computes its determinant and determines the multiplicity of occurring characters. These results are based on a formula giving the number of primitive real characters (mod \(I\)), which corrects proposition 6.6 in the book of the reviewer [Elementary and analytic theory of algebraic numbers. Warszawa: PWN -- Polish Scientific Publishers (1974; Zbl 0276.12002)] in the proof of which certain cases were left out by an oversight.