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Two sharp inequalities for the norm of a factor of a polynomial

Part of: Geometric function theory

Published online by Cambridge University Press:  26 February 2010

David W. Boyd
David W. Boyd
Affiliation:
Department of Mathematics, The University of British Columbia, 121-1984 Mathematics Road, Vancouver, B.C., Canada V6T 1Y4.
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Abstract

Let f(x) be a monic polynomial of degree n with complex coefficients, which factors as f(x) = g(x)h(x), where g and h are monic. Let be the maximum of on the unit circle. We prove that , where β = M(P0) = 1 38135 …, where P0 is the polynomial P0(x, y) = 1 + x + y and δ = M(P1) = 1 79162…, where P1(x, y) = 1 + x + y - xy, and M denotes Mahler's measure. Both inequalities are asymptotically sharp as n → ∞.

MSC classification

Secondary: 30C10: Polynomials
Type
Research Article
Information
Mathematika , Volume 39 , Issue 2 , December 1992 , pp. 341 - 349
Copyright
Copyright © University College London 1992

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