English

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}
}
R2 v1 2026-06-21T17:26:18.753Z