Euler Maclaurin with remainder for a simple integral polytope

Abstract

We give an Euler Maclaurin formula with remainder for the sum of the values of a smooth function on the integral points in a simple integral polytope. This formula is proved by elementary methods.

25 pages. Also see our previous paper in Proc. Nat. Acad. Sci. 100 no. 2 (2003), 426-433. Revision: added Euler Maclaurin formulas for symbols and for polynomials