The Reciprocity Law for Dedekind Sums via the constant Ehrhart coefficient

Details The Reciprocity Law for Dedekind Sums via the constant Ehrhart coefficient The Reciprocity Law for Dedekind Sums via the constant Ehrhart coefficient

2003-05-28

arxiv.org/abs/math/0305404v1

American Mathematical Monthly 106, no. 5 (1999), 459--462

Mathematics

Number Theory

Scientific paper

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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