Units, polyhedra, and a conjecture of Satake

Paul E. Gunnells; Jacob Sturm

Units, polyhedra, and a conjecture of Satake

Number Theory 2007-05-23 v1 Algebraic Geometry

Authors: Paul E. Gunnells , Jacob Sturm

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.

Keywords

rational maps rational functions conjectures and proofs

Cite

@article{arxiv.math/0206217,
  title  = {Units, polyhedra, and a conjecture of Satake},
  author = {Paul E. Gunnells and Jacob Sturm},
  journal= {arXiv preprint arXiv:math/0206217},
  year   = {2007}
}

Comments

plain tex, uses epsf

Units, polyhedra, and a conjecture of Satake

Abstract

Keywords

Cite

Comments

Related papers