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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On products of polynomials

Authors: D. W. Masser and J. Wolbert
Journal: Proc. Amer. Math. Soc. 117 (1993), 593-599
MSC: Primary 11C08
MathSciNet review: 1111220
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Abstract: For a complex polynomial $ P$ in a single variable, let $ H(P)$ be the maximum of the absolute values of its coefficients. Given nonnegative integers $ {n_1}$ and $ {n_2}$, it is well known that $ \mu ({n_1},{n_2}) = \inf \,H({P_1}{P_2})/(H({P_1})H({P_2})) > 0$, where the infimum is taken over all such polynomials $ {P_1}$ and $ {P_2}$ of degrees $ {n_1}$ and $ {n_2}$ respectively. We determine here the exact values of $ \mu (1,n)$ for every $ n$.

References [Enhancements On Off] (What's this?)

  • [G] A. O. Gel′fond, Transcendental and algebraic numbers, Translated from the first Russian edition by Leo F. Boron, Dover Publications, Inc., New York, 1960. MR 0111736
  • [S] Solution to problem E2217, Amer. Math. Monthly 78 (1971), 79.

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Article copyright: © Copyright 1993 American Mathematical Society