On products of polynomials
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- by D. W. Masser and J. Wolbert PDF
- Proc. Amer. Math. Soc. 117 (1993), 593-599 Request permission
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
- A. O. Gel′fond, Transcendental and algebraic numbers, Dover Publications, Inc., New York, 1960. Translated from the first Russian edition by Leo F. Boron. MR 0111736 Solution to problem E2217, Amer. Math. Monthly 78 (1971), 79.
Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 117 (1993), 593-599
- MSC: Primary 11C08
- DOI: https://doi.org/10.1090/S0002-9939-1993-1111220-1
- MathSciNet review: 1111220