The Euler-Maclaurin formula for simple integral polytopes.

Karshon, Yael; Sternberg, Shlomo; Weitsman, Jonathan · Proc Natl Acad Sci U S A · 2003

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Abstract

We give a Euler-Maclaurin formula with remainder for the sum of a smooth function on the integral points in a simple integral lattice polytope. Our proof uses elementary methods.