Interlacing Ehrhart Polynomials of Reflexive Polytopes
  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. 
Akihiro Higashitani, Mario Kummer, Mateusz Micha{\l}ek
math.CO