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arXiv · 2207.11840

Möbius orthogonality of Thue-Morse sequence along Piatetski-Shapiro numbers

Andrei Shubin
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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.

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Andrei Shubin. 2022-07-24. Möbius orthogonality of Thue-Morse sequence along Piatetski-Shapiro numbers. https://arxiv.org/abs/2207.11840

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