On the Ohno-Nakagawa Theorem

In this paper we give a new proof of the Ohno-Nakagawa Theorem using the techniques of L-series. By applying Eisenstein's parametrization of binary cubic forms on the one hand, and a class field theory interpretation of Datskovsky & Wright's Theorem on the other, we reduce the Ohno-Nakagawa Theorem to an identity involving the L-series and the truncated L-series of quadratic orders. We prove this identity by establishing a general relation among these two types L-series.