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4 papers
Mixed toric residues and tropical degenerations
Andras Szenes, Michele Vergne
Building on our earlier work on toric residues and reduction, we give a proof for the mixed toric residue conejecture of Batyrev and Materov. We simplify and streamline our techniq…
Residue formulae for vector partitions and Euler-MacLaurin sums
Andras Szenes, Michele Vergne
Given a finite set of vectors spanning a lattice and lying in a halfspace of a real vector space, to each vector in this vector space one can associate a polytope consisting of…
Arrangements of hyperplanes I: Rational functions and Jeffrey-Kirwan residue
Michel Brion, Michele Vergne
Consider the space of rational functions of several variables with poles on a fixed arrangement of hyperplanes. We obtain a decomposition of as a module over the ri…
Arrangements of hyperplanes II: Szenes formula and Eisenstein series
Michel Brion, Michele Vergne
The aim of this article is to generalize in several variables some formulae for Eisenstein series in one variable. For example the formula $2ζ(2k) = (2π)^{2k} \frac{B_{2k}}{(2k)!}…