q-Ehrhart polynomials of Gorenstein polytopes,\\Bernoulli umbra and related Dirichlet series
Polynômes de q-Ehrhart des polytopes de Gorenstein, ombres de Bernoulli et séries de Dirichlet associées
Résumé
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 Ψ (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
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