E104-05 - Forschungsbereich Kombinatorik und Algorithmen
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Journal:
Mathematika
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ISSN:
0025-5793
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Date (published):
Jan-2019
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Number of Pages:
23
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Publisher:
WILEY
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Peer reviewed:
Yes
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Keywords:
General Mathematics
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Abstract:
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 < 2we 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.
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Research Areas:
außerhalb der gesamtuniversitären Forschungsschwerpunkte: 100%
