On the non-archimedean metric Mahler measure

DOI10.1016/J.JNT.2008.12.009zbMath1196.11143arXiv1408.5084OpenAlexW2068524354MaRDI QIDQ1024539

Charles L. Samuels, Paul Fili

Publication date: 17 June 2009

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1408.5084

zbMATH Keywords

Mahler measureWeil heightLehmer's problem

Mathematics Subject Classification ID

Polynomials (irreducibility, etc.) (11R09) Algebraic numbers; rings of algebraic integers (11R04)

Related Items (8)

The \(t\)-metric Mahler measures of surds and rational numbers ⋮ Metric Mahler measures over number fields ⋮ Norms extremal with respect to the Mahler measure ⋮ Two inequalities on the areal Mahler measure ⋮ The parametrized family of metric Mahler measures ⋮ Metric heights on an abelian group ⋮ THE FINITENESS OF COMPUTING THE ULTRAMETRIC MAHLER MEASURE ⋮ Orthogonal decomposition of the space of algebraic numbers and Lehmer's problem

Cites Work

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• Factorization of certain cyclotomic functions
• On metric heights
• Length of the sum and product of algebraic numbers
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• On a question of Lehmer and the number of irreducible factors of a polynomial
• Addendum to the paper "On the product of the conjugates outside the unit circle of an algebraic number"
• Perturbing polynomials with all their roots on the unit circle
• A Banach space determined by the Weil height
• On the Product of the Conjugates outside the unit circle of an Algebraic Integer
• On the Distribution of the Roots of a Polynomial with Integral Coefficients
• On the metric Mahler measure

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