On the metric Mahler measure

DOI10.1006/JNTH.2000.2579zbMath1030.11056OpenAlexW2002161061MaRDI QIDQ5929412

Christopher J. Smyth, Arturas Dubickas

Publication date: 19 February 2004

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

Full work available at URL: https://semanticscholar.org/paper/a795b2632914ce855e4cf085de9acf385706f77d

zbMATH Keywords

Lehmer's conjectureMahler measurePisot numbersSalem numbers

Mathematics Subject Classification ID

Polynomials (irreducibility, etc.) (11R09) Algebraic numbers; rings of algebraic integers (11R04) PV-numbers and generalizations; other special algebraic numbers; Mahler measure (11R06)

Related Items (15)

On metric heights ⋮ Length of the sum and product of algebraic numbers ⋮ Continued fraction expansions in connection with the metric Mahler measure ⋮ The \(t\)-metric Mahler measures of surds and rational numbers ⋮ Metric Mahler measures over number fields ⋮ Counting exceptional points for rational numbers associated to the Fibonacci sequence ⋮ 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 ⋮ On the non-archimedean metric Mahler measure ⋮ A polynomial time test to detect numbers with many exceptional points ⋮ Optimal factorizations of rational numbers using factorization trees

Cites Work

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• Heights of polynomials and entropy in algebraic dynamics
• Factorization of certain cyclotomic functions
• Conjugate algebraic integers on a circle
• Speculations Concerning the Range of Mahler's Measure
• An effective lower bound for the height of algebraic numbers
• Sums of Fractions with Bounded Numerators

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