Problems Around Polynomials: The Good, The Bad and The Ugly...
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Brändén, P., Krasikov, I., Shapiro, B.: Elements of Pólya–Schur theory in finite diffrence setting (2012). arXiv:1204.2963
Choi, M.-D., Lam, T.-Y., Reznick, B.: Real zeros of positive definite forms. I. Math. Z. 171, 1–26 (1980)
De Loera, J.A., McAllister, T.B.: Vertices of Gelfand–Tsetlin polytopes (2003). arXiv:math/0309329
Fisk, S.: Polynomials, roots, and interlacing (2006). arXiv:math/0612833
Forsgård, J., Kostov, Vl., Shapiro, B.: Could René Descartes have known this? (2015). arXiv:1501.00856
Forsgård, J.: Shapiro, B.: Discriminant amoebas, complex zero decreasing sequences, and the Karlin problem (2015). (In preparation)
Gabrielov, A., Novikov, D., Shapiro, B.: Mystery of point charges. Proc. Lond. Math. Soc. (3) 95(2), 443–472 (2007)
Killian, K.: A remark on Maxwell’s conjecture for planar charges. Complex Var. Elliptic Equations 54(12), 1073–1078 (2009)
Kostov, V., Shapiro, B., Tyaglov, M.: Maximal univalent disks of real rational functions and Hermite–Biehler polynomials. Proc. Am. Math. Soc. 139(5), 1625–1635 (2011)
Langer, R.E.: On the zeros of exponential sums and integrals. Bull. Am. Math. Soc. 37, 213–239 (1931)
Maxwell, J.C.: A treatise on electricity and magnetism. In: Republication of the 3rd revised edition, vol. 1. Dover Publ. Inc., (1954)
Oleinik, O.A., Petrovskii, I.G.: On the topology of real algebraic hypersurfaces (Russian). Izv. Acad. Nauk SSSR 13, 389–402 (1949). [English transl.: Am. Math. Soc. Transl. 7, 399–417 (1962)]
Peretz, R.: Application of the argument principle to Maxwell’s conjecture for three point charges. Complex Var. Elliptic Equations 58(5), 1–11 (2013)
Shapiro, B., Shapiro, M.: A few riddles behind Rolle’s theorem. Am. Math. Mon. 119(9), 787–793 (2012)
Tyaglov, M.: On the number of real critical points of logarithmic derivatives and the Hawaii conjecture. J. Anal. Math. 114, 1–62 (2011)
Wang, Y.: Equilibrium points of potential fields produced by positive point charges. http://ccs.math.ucsb.edu/senior-thesis/YifeiWang (2012)