Binary constant-length substitutions and mahler measures of Borwein polynomials

Title: Binary constant-length substitutions and mahler measures of Borwein polynomials
Creator: Baake, Michael; Coons, Michael; Manibo, Neil
Relation: From Analysis to Visualization: A Celebration of the Life and Legacy of Jonathan M. Borwein. Jonathan M. Borwein Commemorative Conference, JBCC 2017 (Newcastle, Australia 25-29 September, 2017) p. 303-322
Publisher Link: http://dx.doi.org/10.1007/978-3-030-36568-4_20
Publisher: Springer
Resource Type: conference paper
Date: 2020
Description: We show that the Mahler measure of every Borwein polynomial—a polynomial with coefficients in {−1,0,1} having non-zero constant term—can be expressed as a maximal Lyapunov exponent of a matrix cocycle that arises in the spectral theory of binary constant-length substitutions. In this way, Lehmer’s problem for height-one polynomials having minimal Mahler measure becomes equivalent to a natural question from the spectral theory of binary constant-length substitutions. This supports another connection between Mahler measures and dynamics, beyond the well-known appearance of Mahler measures as entropies in algebraic dynamics.
Subject: binary substitutions; Mahler measure; Lyapunov exponents; polynomials; spectral theory
Identifier: http://hdl.handle.net/1959.13/1465187
Identifier: uon:47228
Identifier: ISBN:9783030365684
Language: eng
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