It was observed by Bump et al. that Ehrhart polynomials in a special family
exhibit properties similar to the Riemann {\zeta} function. The construction
was generalized by Matsui et al. to a larger family of reflexive polytopes
coming from graphs. We prove several conjectures confirming when such
polynomials have zeros on a certain line in the complex plane. Our main new
method is to prove a stronger property called interlacing

Higashitani, Akihiro