  This article considers some q-analogues of classical results concerning the
Ehrhart polynomials of Gorenstein polytopes, namely properties of their
q-Ehrhart polynomial with respect to a good linear form. Another theme is a
specific linear form {\Psi} (involving Carlitz' q-analogues of Bernoulli
numbers) on the space of polynomials, for which one shows interesting behaviour
on these q-Ehrhart polynomials. A third point is devoted to some related
zeta-like functions associated with polynomials
