Lattice polytopes, Hecke operators, and the Ehrhart polynomial
  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. 
Paul E. Gunnells, Fernando Rodriguez Villegas