اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدBinary constant-length substitutions and Mahler measures of Borwein polynomials
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تأليف
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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