On Mahler’s measure of a polynomial
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- by Alain Durand PDF
- Proc. Amer. Math. Soc. 83 (1981), 75-76 Request permission
Abstract:
Let $P$ be a polynomial with complex coefficients. We denote by $M(P)$ the Mahler measure of $P$ (resp. the maximum modulus of $P$ on the disk $\left | z \right | \leqslant 1)$). We prove here that $M(P) = \inf \left \| {PQ} \right \|$ where the infimum is taken over all polynomials $Q$ with complex coefficients satisfying $Q(0) = 1$.References
- Wayne Lawton, Heights of algebraic numbers and Szegő’s theorem, Proc. Amer. Math. Soc. 49 (1975), 47–50. MR 376628, DOI 10.1090/S0002-9939-1975-0376628-X
- K. Mahler, An application of Jensen’s formula to polynomials, Mathematika 7 (1960), 98–100. MR 124467, DOI 10.1112/S0025579300001637
Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 83 (1981), 75-76
- MSC: Primary 30C10
- DOI: https://doi.org/10.1090/S0002-9939-1981-0619985-1
- MathSciNet review: 619985