arXiv 1102.29712011-02math.NT

Spiegelungssatz: a combinatorial proof for the 4-rank

Laurent Habsieger, Emmanuel Royer

发表信息：: International Journal of Number Theory (2011) 12 pages

英文摘要：

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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