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

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- by Michel Brion and Michèle Vergne
- J. Amer. Math. Soc.
**10**(1997), 797-833 - DOI: https://doi.org/10.1090/S0894-0347-97-00242-7
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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.## References

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## Bibliographic Information

**Michel Brion**- Affiliation: Institut Fourier, B.P. 74, 38402 Saint-Martin d’Hères Cedex, France
- MR Author ID: 41725
- Email: mbrion@fourier.ujf-grenoble.fr
**Michèle Vergne**- Affiliation: École Normale Supérieure, 45 rue d’Ulm, 75005 Paris Cedex 05, France
- MR Author ID: 177945
- Email: vergne@dmi.ens.fr
- Received by editor(s): December 30, 1996
- Received by editor(s) in revised form: March 28, 1997
- © Copyright 1997 American Mathematical Society
- Journal: J. Amer. Math. Soc.
**10**(1997), 797-833 - MSC (1991): Primary 11P21, 52B20
- DOI: https://doi.org/10.1090/S0894-0347-97-00242-7
- MathSciNet review: 1446364