Deshouillers, J.-M., Drmota, M., Müllner, C., Shubin, A., & Spiegelhofer, L. (2022). Synchronizing automatic sequences along Piatetski-Shapiro sequences. arXiv. https://doi.org/10.48550/arXiv.2211.01422
E104-05 - Forschungsbereich Kombinatorik und Algorithmen
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ArXiv ID:
2211.01422
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Date (published):
2022
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Number of Pages:
32
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Preprint Server:
arXiv
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Keywords:
Automatic sequences; Piatetski-Shapiro sequences
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Abstract:
The purpose of this paper is to study subsequences of synchronizing k-automatic sequences a(n) along Piatetski-Shapiro sequences ⌊nc⌋ with non-integer c>1. In particular, we show that a(⌊n^c⌋) satisfies a prime number theorem of the form ∑_{n≤x} Λ(n)a(⌊n^c⌋)∼Cx, and, furthermore, that it is deterministic for c∈ℝ∖ℤ. As an interesting additional result, we show that the sequence ⌊nc⌋modm has polynomial subword complexity.
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Project title:
Arithmetische Zufälligkeit: I 4945-N (FWF - Österr. Wissenschaftsfonds)
