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

Abstract : 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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Submitted on : Wednesday, July 30, 2014 - 2:08:47 PM
Last modification on : Monday, April 15, 2019 - 12:15:56 PM
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  • HAL Id : hal-01053353, version 1
  • ARXIV : 1408.1329

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Frédéric Chapoton, Driss Essouabri. q-Ehrhart polynomials of Gorenstein polytopes,\\Bernoulli umbra and related Dirichlet series. 2014. ⟨hal-01053353⟩

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