Record link: 
http://hdl.handle.net/20.500.12708/190364
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Title: 
Coprimality of Consecutive Elements in a Piatetski-Shapiro Sequence
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Citation: 
Deshouillers, J.-M., Drmota, M., & Müllner, C. (2023). Coprimality of Consecutive Elements in a Piatetski-Shapiro Sequence. In H. Maier, J. Steuding, & R. Steuding (Eds.), Number Theory in Memory of Eduard Wirsing (pp. 91–98). Springer. https://doi.org/10.1007/978-3-031-31617-3_7
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Publisher DOI: 
10.1007/978-3-031-31617-3_7
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Publication Type: 
Book Contribution - Edited Volume Contribution
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Language: 
English
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Authors: 
Deshouillers , Jean-Marc 
Drmota, Michael 
Müllner, Clemens 
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Organisational Unit: 
E104-05 - Forschungsbereich Kombinatorik und Algorithmen 
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Published in: 
Number Theory in Memory of Eduard Wirsing 
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ISBN: 
978-3-031-31617-3
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Date (published): 
2023
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Number of Pages: 
8
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Publisher: 
Springer, Cham
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Keywords: 
Piatetski-Shapiro sequences; coprimality; congruences; distribution modulo 1; trigonometric sums
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Abstract: 
We show that in any Piatetski-Shapiro sequence with c in , there exist long subsequences of consecutive elements no pair of which are coprime, whereas for any c in , there exist infinitely many n such that all the elements in are pairwise coprime for H almost as large as .
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Project title: 
Arithmetische Zufälligkeit: I 4945-N (FWF - Österr. Wissenschaftsfonds) 
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Research Areas: 
Fundamental Mathematics Research: 100%
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Science Branch: 
1010 - Mathematik: 100%
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Appears in Collections:
Book Contribution

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