Abstract: Let P be a simple lattice polytope. We define an action of the Hecke operators on E (P), the Ehrhart polynomial of P, and describe their effect on the coefficients of E (P). We also describe how the Brion-Vergne formula transforms under the Hecke operators for nonsingular lattice polytopes P.

BibTeX

@misc{math.CO/??,
    title = {{Lattice polytopes, Hecke operators, and the Ehrhart polynomial}}.
    author = {Paul E. Gunnells and Fernando Rodriguez Villegas},
    eprint = {preprint, 2004}}