Units, polyhedra, and a conjecture of Satake

Details Units, polyhedra, and a conjecture of Satake Units, polyhedra, and a conjecture of Satake

2002-06-20

arxiv.org/abs/math/0206217v1

Mathematics

Number Theory

plain tex, uses epsf

Scientific paper

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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