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Register a new userBinary constant-length substitutions and Mahler measures of Borwein polynomials
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Michael Baake
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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, Lehmers 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.
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Jonathan M. Borwein (1951-2016) was a prolific mathematician whose career spanned several countries (UK, Canada, USA, Australia) and whose many interests included analysis, optimisation, number theory, special functions, experimental mathematics, mathematical finance, mathematical education, and visualisation. We describe his life and legacy, and give an annotated bibliography of some of his most significant books and papers.
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