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Proceedings of the American Mathematical Society

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

 
 

 

On Mahler's measure of a polynomial


Author: Alain Durand
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
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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\vert z \right\vert \leqslant 1)$). We prove here that $ M(P) = \inf \left\Vert {PQ} \right\Vert$ where the infimum is taken over all polynomials $ Q$ with complex coefficients satisfying $ Q(0) = 1$.


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DOI: https://doi.org/10.1090/S0002-9939-1981-0619985-1
Keywords: Mahler's measure, Jensen's theorem, maximum modulus principle
Article copyright: © Copyright 1981 American Mathematical Society

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