Spiegelungssatz: a combinatorial proof for the 4-rank

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.

Article de revue

International Journal of Number Theory 7, No. 8, 2157-2170