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ISSN 1088-6834(e) ISSN 0894-0347(p)

Residue formulae, vector partition functions and lattice points in rational polytopes

Author(s): Michel Brion; Michèle Vergne
Journal: J. Amer. Math. Soc. 10 (1997), 797-833.
MSC (1991): Primary 11P21, 52B20
MathSciNet review: 1446364
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Abstract: We obtain residue formulae for certain functions of several variables. As an application, we obtain closed formulae for vector partition functions and for their continuous analogs. They imply an Euler-MacLaurin summation formula for vector partition functions, and for rational convex polytopes as well: we express the sum of values of a polynomial function at all lattice points of a rational convex polytope in terms of the variation of the integral of the function over the deformed polytope.

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