Local Euler-Maclaurin formula for polytopes

By N. Berline, Michèle Vergne. 2005

89 citations recorded by the source corpus.

We give a local Euler-Maclaurin formula for rational convex polytopes in a rational euclidean space . For every affine rational polyhedral cone C in a rational euclidean space W, we construct a differential operator of infinite order D(C) on W with constant rational coefficients, which is unchanged when C is translated by an integral vector. Then for every convex rational polytope P in a rational euclidean space V and every polynomial function f (x) on V, the sum of the values of f(x) at the integral points of P is equal to the sum, for all faces F of P, of the integral over F of the function D(N(F)).f , where we denote by N(F) the normal cone to P along F.

Subfields: Applied Mathematics, Pharmacology

View Paper: https://www.semanticscholar.org/paper/852c0bfae1b343fce03d7417718915fc10875d38

Citations in the corpus

• Applications of Equivariant Cohomology (2006, unknown): “The detailed statement for any rational convex polytope and what we really mean by “depending only on” is in [17].”