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Units, polyhedra, and a conjecture of Satake

Paul E. Gunnells·Jacob Sturm
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Abstract

Let $F/\QQ $ be a totally real number field of degree $n$. We explicitly evaluate a certain sum of rational functions over a infinite fan of $F$-rational polyhedral cones in terms of the norm map $\Norm \colon F\to \QQ $. This completes Sczech's combinatorial proof of Satake's conjecture connecting the special values of $L$-series associated to cusp singularities with intersection numbers of divisors in their toroidal resolutions.

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Paul E. Gunnells, Jacob Sturm. 2002-06-20. Units, polyhedra, and a conjecture of Satake. https://arxiv.org/abs/math/0206217

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