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.

• Paul E. Gunnells ^[1] ; Fernando Rodriguez Villegas ^[2]
  1. [1] University of Massachusetts
  2. [2] University of Texas
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 13, Nº. 2, 2007, págs. 253-276
• Idioma: inglés
• DOI: 10.1007/s00029-007-0037-5
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  • 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.