Units, polyhedra, and a conjecture of Satake
Paul E. Gunnells, Jacob Sturm
Abstract
Let F/ 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 F . 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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