Abstract
It was observed by Bump et al. that Ehrhart polynomials in a special family exhibit properties shared by 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.
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Akihiro Higashitani is partially supported by JSPS Grant-in-Aid for Young Scientists (B) 26800015.
Mateusz Michałek is supported by the Polish National Science Center Grant 2013/08/A/ST1/00804.
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Higashitani, A., Kummer, M. & Michałek, M. Interlacing Ehrhart polynomials of reflexive polytopes. Sel. Math. New Ser. 23, 2977–2998 (2017). https://doi.org/10.1007/s00029-017-0350-6
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DOI: https://doi.org/10.1007/s00029-017-0350-6