On the Ohno-Nakagawa Theorem

Xia Gao

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arXiv · 1608.00803

On the Ohno-Nakagawa Theorem

Xia Gao

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Abstract

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.

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Xia Gao. 2016-08-02. On the Ohno-Nakagawa Theorem. https://arxiv.org/abs/1608.00803

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