ZEROS OF CERTAIN POLYNOMIALS

By M. Gulzar, A. Manzoor. 2016

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Ehrhart polynomials and successive minima (2005, background): “rom a much more general result of Bump et al. [12, Theorem 4] that the zeros of G(s,C∗ n) all have real parts equal to −1/2. They also prove the functional equation G(−s,C∗ n) = (−1)nG(s−1,C∗ n) (cf. [36]). Next we note that for two lattice polytopes P1 ∈ Pn1, P2 ∈ Pn2 living in complementary spaces”
COEFFICIENTS AND ROOTS OF EHRHART POLYNOMIALS (2004, background): “[3] and Rodriguez [16] proved that the zeros of iOd all have real parts equal to −1/2.”
Roots of Ehrhart polynomials arising from graphs (2010, unknown): “It then follows from the well-known theorem [26] that if G is tree, the real parts of all the roots of i(P ± G,m) are equal to − (1)2 .”