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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.83.

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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


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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Bibliographic Information
  • Michel Brion
  • Affiliation: Institut Fourier, B.P. 74, 38402 Saint-Martin d’Hères Cedex, France
  • MR Author ID: 41725
  • Email:
  • Michèle Vergne
  • Affiliation: École Normale Supérieure, 45 rue d’Ulm, 75005 Paris Cedex 05, France
  • MR Author ID: 177945
  • Email:
  • 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:
  • MathSciNet review: 1446364