Strong divisibility sequences and sieve methods
Browning TD, Verzobio M. 2024. Strong divisibility sequences and sieve methods. Mathematika. 70(4), e12269.
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Abstract
We investigate strong divisibility sequences and produce lower and upper bounds for the density of integers in the sequence that only have (somewhat) large prime factors. We focus on the special cases of Fibonacci numbers and elliptic divisibility sequences, discussing the limitations of our methods. At the end of the paper, there is an appendix by Sandro Bettin on divisor closed sets that we use to study the density of prime terms that appear in strong divisibility sequences.
Publishing Year
Date Published
2024-07-23
Journal Title
Mathematika
Acknowledgement
The authors are very grateful to Andrew Granville, Dimitris Koukoulopoulos, Davide Lombardo,Florian Luca, Igor Shparlinski and Joni Teräväinen for useful comments. While working on thispaper, the first author was supported by a FWF Grant (DOI 10.55776/P36278) and the secondauthor was supported by the European Union’s Horizon 2020 research and innovation programunder the Marie Skłodowska-Curie Grant Agreement Number 101034413.
Volume
70
Issue
4
Article Number
e12269
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eISSN
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Cite this
Browning TD, Verzobio M. Strong divisibility sequences and sieve methods. Mathematika. 2024;70(4). doi:10.1112/mtk.12269
Browning, T. D., & Verzobio, M. (2024). Strong divisibility sequences and sieve methods. Mathematika. London Mathematical Society. https://doi.org/10.1112/mtk.12269
Browning, Timothy D, and Matteo Verzobio. “Strong Divisibility Sequences and Sieve Methods.” Mathematika. London Mathematical Society, 2024. https://doi.org/10.1112/mtk.12269.
T. D. Browning and M. Verzobio, “Strong divisibility sequences and sieve methods,” Mathematika, vol. 70, no. 4. London Mathematical Society, 2024.
Browning TD, Verzobio M. 2024. Strong divisibility sequences and sieve methods. Mathematika. 70(4), e12269.
Browning, Timothy D., and Matteo Verzobio. “Strong Divisibility Sequences and Sieve Methods.” Mathematika, vol. 70, no. 4, e12269, London Mathematical Society, 2024, doi:10.1112/mtk.12269.
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