2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64355Let $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.plain tex, uses epsfNumber TheoryAlgebraic Geometry11F41; 11R42; 14M25text