Olga Aryasova (Inst. of Geophysics, Nat. Acad. of Sciences of Ukraine / Friedrich–Schiller–Univ. Jena)
Mateo Spriet (Uni Toulouse)
The classical Euler-MacLaurin formula links the sum over integers of a single variable real function with its integral. In their article "Local Euler-MacLaurin formula for polytopes", Nicole Berline and Michèle Vergne generalize this relation to higher dimensions. Based on this article and on the book "Integer Points in Polyhedra" from Alexander Barvinok, we will derive this formula in the case of the exponential function, which will link discrete and continuous Laplace transforms of a given polyhedron. As a consequence we will give a formula that relates the number of lattice points of a polytope with the volume of its faces.
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