On the Ohno-Nakagawa Theorem
Number Theory
2016-08-03 v1
Abstract
In this paper we give a new proof of the Ohno-Nakagawa Theorem using the techniques of -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 -series and the truncated -series of quadratic orders. We prove this identity by establishing a general relation among these two types -series.
Cite
@article{arxiv.1608.00803,
title = {On the Ohno-Nakagawa Theorem},
author = {Xia Gao},
journal= {arXiv preprint arXiv:1608.00803},
year = {2016}
}