Normality of the Thue--Morse sequence along Piatetski-Shapiro sequences, II

Clemens Müllner, Lukas Spiegelhofer

We prove that the Thue--Morse sequence $\mathbf{t}$ along subsequences indexed by $\lfloor n^c\rfloor$ is normal, where $1<c<3/2$. That is, for $c$ in this range and for each $ω\in\…