Möbius orthogonality of the Thue–Morse sequence along Piatetski-Shapiro numbers
Volume 273 / 2023
Studia Mathematica 273 (2023), 201-238
MSC: Primary 11B50; Secondary 11L07.
DOI: 10.4064/sm220818-3-8
Published online: 14 November 2023
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 $1 \lt c \lt 2$. 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.
