On the behavior of Mahler's measure under iteration

DOI10.1007/s00605-020-01416-5zbMath1450.11110arXiv1911.06288OpenAlexW2983419103MaRDI QIDQ783999

Lukas Pottmeyer, Mingming Zhang, Paul Fili

Publication date: 5 August 2020

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1911.06288

zbMATH Keywords

unitsMahler measurePisot numbersSalem numbersPerron numbers

Mathematics Subject Classification ID

Cubic and quartic extensions (11R16) Polynomials (irreducibility, etc.) (11R09) Algebraic numbers; rings of algebraic integers (11R04) PV-numbers and generalizations; other special algebraic numbers; Mahler measure (11R06)

Related Items (3)

Mahler measures of Pisot and Salem type numbers ⋮ Wandering points for the Mahler measure ⋮ On the frequency of height values

Cites Work

• Additive and multiplicative relations connecting conjugate algebraic numbers
• Factorization of certain cyclotomic functions
• On numbers which are Mahler measures
• Lehmer's problem for polynomials with odd coefficients
• Salem numbers as Mahler measures of nonreciprocal units
• Entropies and factorizations of topological Markov shifts
• Mahler Measures Close to an Integer
• Mahler measure on Galois extensions
• On a question of Lehmer and the number of irreducible factors of a polynomial
• The entropies of topological Markov shifts and a related class of algebraic integers
• Galois theory of Salem polynomials
• Perron units which are not Mahler measures
• Topological entropy and equivalence of dynamical systems
• Polynomials with small Mahler measure
• On values of the Mahler measure in a quadratic field (solution of a problem of Dixon and Dubickas)
• Minimal Mahler Measures
• The values of Mahler measures
• On the Product of the Conjugates outside the unit circle of an Algebraic Integer

This page was built for publication: On the behavior of Mahler's measure under iteration