Möbius orthogonality of the Thue-Morse sequence along Piatetski-Shapiro numbers. (English) Zbl 07791442
Author’s abstract: We show that the Möbius function is orthogonal to the Thue-Morse sequence \(t(n)\) taken along the Piatetski-Shapiro numbers \(\lfloor n^c\rfloor\) for any \(1 < c < 2\). Previously, this property was established for the subsequence along the squares \(t(n^2)\). These are both examples of Möbius orthogonal sequences with maximum entropy.
Reviewer: Michel Rigo (Liège)
MSC:
| 11B85 | Automata sequences |
| 11J54 | Small fractional parts of polynomials and generalizations |
| 11L07 | Estimates on exponential sums |
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