Abstract:
Mahler has obtained an inequality for the products of zeros of an algebraic polynomial and its derivative lying outside the unit disc. In this paper a converse inequality with best possible constant is established.
\Bibitem{Sto96}
\by \`E.~A.~Storozhenko
\paper A problem of Mahler on the~zeros of a~polynomial and its derivative
\jour Sb. Math.
\yr 1996
\vol 187
\issue 5
\pages 735--744
\mathnet{http://mi.mathnet.ru/eng/sm130}
\crossref{https://doi.org/10.1070/SM1996v187n05ABEH000130}
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\zmath{https://zbmath.org/?q=an:0866.30009}
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This publication is cited in the following 12 articles:
O'Rourke S., Williams N., “Pairing Between Zeros and Critical Points of Random Polynomials With Independent Roots”, Trans. Am. Math. Soc., 371:4 (2019), 2343–2381
Kovalenko L.G., Storozhenko E.A., “on the Fractional Integrodifferentiation of Complex Polynomials in l (0)”, Ukr. Math. J., 69:5 (2017), 823–830
Pritsker I.E., “Inequalities For Integral Norms of Polynomials Via Multipliers”, Progress in Approximation Theory and Applicable Complex Analysis: in Memory of Q.i. Rahman, Springer Optimization and Its Applications, 117, eds. Govil N., Mohapatra R., Qazi M., Schmeisser G., Springer, 2017, 83–103
Sean O'Rourke, “Critical Points of Random Polynomials and Characteristic Polynomials of Random Matrices”, Int Math Res Notices, 2016:18 (2016), 5616
È. A. Storozhenko, L. G. Kovalenko, “Inequality for Fractional Integrals of Complex Polynomials in L0”, Math. Notes, 96:4 (2014), 609–612
Robin Pemantle, Igor Rivin, Advances in Combinatorics, 2013, 259
Dubickas A., Jankauskas J, “On Mahler measures of a self-inversive polynomial and its derivative”, Bulletin of the London Mathematical Society, 42:Part 2 (2010), 195–209
Adamov, AN, “INEQUALITY OF THE TURAN TYPE FOR TRIGONOMETRIC POLYNOMIALS AND CONJUGATE TRIGONOMETRIC POLYNOMIALS IN L-0”, Ukrainian Mathematical Journal, 61:7 (2009), 1169
È. A. Storozhenko, “Turán-type inequalities for complex polynomials in the L0-metric”, Russian Math. (Iz. VUZ), 52:5 (2008), 88–94
Pritsker, IE, “AN AREAL ANALOG OF MAHLER'S MEASURE”, Illinois Journal of Mathematics, 52:2 (2008), 347
È. A. Storozhenko, “Nikol'skii-Stechkin inequality for trigonometric polynomials in L0”, Math. Notes, 80:3 (2006), 403–409
B. S. Kashin, N. P. Korneichuk, P. L. Ul'yanov, I. A. Shevchuk, V. A. Andrienko, “A brief survey of scientific results of E. A. Storozhenko”, Ukr Math J, 52:4 (2000), 531
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