Spiegelungssatz: a combinatorial proof for the 4-rank

Details Spiegelungssatz: a combinatorial proof for the 4-rank Spiegelungssatz: a combinatorial proof for the 4-rank

2011-02-15

arxiv.org/abs/1102.2971v2

International Journal of Number Theory (2011) 12 pages

Mathematics

Number Theory

Scientific paper

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.

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