Lattice polytopes, Hecke operators, and the Ehrhart polynomial
This is the pre-published version harvested from ArXiv. The published version is located at http://www.springerlink.com/content/qr18k61r4j132654/
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 for E(P) transforms under the Hecke operators for nonsingular lattice polytopes P.
PE Gunnells and FR Villegas. "Lattice polytopes, Hecke operators, and the Ehrhart polynomial" Selecta Mathematica-NewSeries 13.2 (2007): 253-276.
Available at: http://works.bepress.com/paul_gunnells/9