q-Ehrhart polynomials of Gorenstein polytopes, Bernoulli umbra and related Dirichlet series (Q326859)

In this article the authors generalize classical results of Ehrhart polynomials on Gorenstein polytopes to \(q\)-Ehrhart polynomials of lattice polytopes. Using Carlitz' \(q\)-analogues of Bernoulli numbers the authors study the values on these polynomials of a specific linear form. Further they introduce a zeta function associated to an Ehrhart polynomial and connect its evaluation at negative integers to \(q\)-analogues of Bernoulli numbers.