Units, polyhedra, and a conjecture of Satake

Units, polyhedra, and a conjecture of Satake Title: Units, polyhedra, and a conjecture of Satake
Author: Paul E. Gunnells and Jacob Sturm

Math Subject Class: 14F

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\rightarrow \QQ $. This completes Sczech's combinatorial proof of Satake's conjecture, which relates the special values of $L$-series associated to cusp singularities with intersection numbers of divisors in their resolutions \cite{Sc2}.

BibTeX

@misc{math.NT/0206217,
    title = {{Units, polyhedra, and a conjecture of Satake}},
    author = {Paul E. Gunnells and Jacob Sturm},
    eprint = {arXiv:math.NT/0206217}}