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The Reciprocity Law for Dedekind Sums via the constant Ehrhart coefficient

Matthias Beck
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Abstract

We obtain a new motivated proof of the reciprocity law for Dedekind sums by computing the constant coefficient of the Ehrhart polynomial for a rectangular triangle in two ways. On the one hand, the constant term is the Euler characteristic, and on the other hand it is given by a cotangent Laurent expansion.

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Matthias Beck. 2003-05-28. The Reciprocity Law for Dedekind Sums via the constant Ehrhart coefficient. https://arxiv.org/abs/math/0305404

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