- 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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