DOIAbstract
Text. The goal of this note is to generalize a formula of Datskovsky and Wright on the zeta function associated with integral binary cubic forms. We show that for a fixed number field K of degree d, the zeta function associated with decomposable forms belonging to K in d - 1 variables can be factored into a product of Riemann and Dedekind zeta functions in a similar fashion. We establish a one-to-one correspondence between the pure module classes of rank d - 1 of K and the integral ideals of width < d - 1. This reduces the problem to counting integral ideals of a special type, which can be solved using a tailored Moebius inversion argument. As a by-product, we obtain a characterization of the conductor ideals for orders of number fields....
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