Gorenstein simplices with a given δ-polynomial

To classify the lattice polytopes with a given delta-polynomial is an important open problem in Ehrhart theory. A complete classification of the Gorenstein simplices whose normalized volumes are prime integers is known. In particular, their delta-polynomials are of the form 1+t(k)+ ... +t((v-1)k). where k and v are positive integers. In the present paper, a complete classification of the Gorenstein simplices with the above delta-polynomials will be performed, when v is either p(2) or pq, where p and q are prime integers with p not equal q. Moreover, we consider the number of Gorenstein simplices, up to unimodular equivalence, with the expected delta-polynomial. (C) 2019 Elsevier B.V. All rights reserved.