Spiegelungssatz: a combinatorial proof for the 4-rank
Number Theory
2011-04-29 v2
Abstract
The Spiegelungssatz is an inequality between the (4)-ranks of the narrow ideal class groups of the quadratic fields (\mathbb{Q}(\sqrt{D})) and (\mathbb{Q}(\sqrt{-D})). We provide a combinatorial proof of this inequality. Our interpretation gives an affine system of equations that allows to describe precisely some equality cases.
Keywords
Cite
@article{arxiv.1102.2971,
title = {Spiegelungssatz: a combinatorial proof for the 4-rank},
author = {Laurent Habsieger and Emmanuel Royer},
journal= {arXiv preprint arXiv:1102.2971},
year = {2011}
}