Interlacing Ehrhart polynomials of reflexive polytopes

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2017
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Higashitani, Akihiro
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It was observed by Bump et al. that Ehrhart polynomials in a special family exhibit properties shared by the Riemann ζ 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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510 Mathematik
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ISO 690HIGASHITANI, Akihiro, Mario KUMMER, Mateusz MICHALEK, 2017. Interlacing Ehrhart polynomials of reflexive polytopes. In: Selecta Mathematica. Birkhäuser bei Springer. 2017, 23(4), pp. 2977-2998. ISSN 1022-1824. eISSN 1420-9020. Available under: doi: 10.1007/s00029-017-0350-6
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@article{Higashitani2017-10Inter-52564,
  year={2017},
  doi={10.1007/s00029-017-0350-6},
  title={Interlacing Ehrhart polynomials of reflexive polytopes},
  number={4},
  volume={23},
  issn={1022-1824},
  journal={Selecta Mathematica},
  pages={2977--2998},
  author={Higashitani, Akihiro and Kummer, Mario and Michalek, Mateusz}
}
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