M\"obius orthogonality of Thue-Morse sequence along Piatetski-Shapiro numbers
Abstract
We show that the M\"obius function is orthogonal to the Thue-Morse sequence t(n) taken along the Piatetski-Shapiro numbers nc for any 1 < c < 2. Previously this property was established for the subsequence along the squares t(n2). These are both examples of M\"obius orthogonal sequences with maximum entropy.
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