On the zeros of certain polynomials

On the zeros of certain polynomials
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by Fernando Rodriguez-Villegas PDF

Proc. Amer. Math. Soc. 130 (2002), 2251-2254 Request permission

We prove that certain naturally arising polynomials have all of their roots on a vertical line.

References

Daniel Bump, Kwok-Kwong Choi, Pär Kurlberg, and Jeffrey Vaaler, A local Riemann hypothesis. I, Math. Z. 233 (2000), no. 1, 1–19. MR 1738342, DOI 10.1007/PL00004786
J. Harer and D. Zagier, The Euler characteristic of the moduli space of curves, Invent. Math. 85 (1986), no. 3, 457–485. MR 848681, DOI 10.1007/BF01390325
G. Pólya and G. Szegő, Problems and theorems in analysis. Vol. II, Revised and enlarged translation by C. E. Billigheimer of the fourth German edition, Die Grundlehren der mathematischen Wissenschaften, Band 216, Springer-Verlag, New York-Heidelberg, 1976. Theory of functions, zeros, polynomials, determinants, number theory, geometry. MR 0396134
A. Postnikov and R. Stanley, Deformations of Coxeter Hyperplane Arrangements, J. Combin. Theory Ser. A 91 (2000), 544–597.
N. Obreschkov, Lösung der Aufgabe 35, Section 2, Jahresber. Deutsch. Math. Verein. 36 (1917), 43–45.
Richard P. Stanley, Hilbert functions of graded algebras, Advances in Math. 28 (1978), no. 1, 57–83. MR 485835, DOI 10.1016/0001-8708(78)90045-2
Richard P. Stanley, Combinatorics and commutative algebra, Progress in Mathematics, vol. 41, Birkhäuser Boston, Inc., Boston, MA, 1983. MR 725505, DOI 10.1007/978-1-4899-6752-7