[Zurück]

M. Drmota, J. Deshouillers, L. Spiegelhofer, C. Müllner:
"Randomness and non-randomness properties of Piatetski-Shapiro sequences modulo m";
Mathematika, 65 (2019), 4; S. 1051 - 1073.

We study Piatetski-Shapiro sequences [n^c] modulo m, for non-integers c > 1 an positive m,

and we are particularly interested in subword occurrences in those sequences.
We prove that each block \in \{0,1\}^k of length k < c+1 occurs as a subword with the frequency 2^{-k},
while there are always blocks that do not occur. In particular, those sequences are not normal. For 1 < c < 2
we estimate the number of subwords from above and below, yielding the fact that our sequences are deterministic and not morphic. Finally, using the Daboussi-Kátai criterion, we prove that the sequence [n^c] modulo m
is asymptotically orthogonal to multiplicative functions bounded by 1 and with mean value 0.

http://dx.doi.org/10.1112/S0025579319000287