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

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