The Euler-Maclaurin formula for simple integral polytopes

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The Euler-Maclaurin formula for simple integral polytopes.

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.

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Local Euler-Maclaurin formula for polytopes

(with DF = 1 for F = P). As explained in [2], essential properties required on the operators DF are ”locality” and ”computability”. At each face F of P, the operator DF should depend only of the translation class modulo Z of the normal cone No(P, F ) to P at a generic point of F (if F is of codimension k, the normal cone is an affine cone of dimension k). In particular if P is an integral polyt...

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ژورنال

عنوان ژورنال: Proceedings of the National Academy of Sciences

سال: 2003

ISSN: 0027-8424,1091-6490

DOI: 10.1073/pnas.0237168100