Computing the volume, counting integral points, and exponential sums

Abstract

We design polynomial-time algorithms for some particular cases of the volume computation problem and the integral points counting problem for convex polytopes. The basic idea is a reduction to the computation of certain exponential sums and integrals. We give elementary proofs of some known identities between these sums and integrals and prove some new identities. © 1993 Springer-Verlag New York Inc.