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arXiv · 1102.2971

Spiegelungssatz: a combinatorial proof for the 4-rank

Laurent Habsieger·Emmanuel Royer
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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.

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Laurent Habsieger, Emmanuel Royer. 2011-02-15. Spiegelungssatz: a combinatorial proof for the 4-rank. https://arxiv.org/abs/1102.2971

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