{"quality_controlled":"1","article_processing_charge":"Yes (via OA deal)","scopus_import":"1","title":"Strong divisibility sequences and sieve methods","article_type":"original","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1112/mtk.12269"}],"publisher":"London Mathematical Society","corr_author":"1","volume":70,"ec_funded":1,"date_published":"2024-07-23T00:00:00Z","citation":{"chicago":"Browning, Timothy D, and Matteo Verzobio. “Strong Divisibility Sequences and Sieve Methods.” <i>Mathematika</i>. London Mathematical Society, 2024. <a href=\"https://doi.org/10.1112/mtk.12269\">https://doi.org/10.1112/mtk.12269</a>.","ista":"Browning TD, Verzobio M. 2024. Strong divisibility sequences and sieve methods. Mathematika. 70(4), e12269.","short":"T.D. Browning, M. Verzobio, Mathematika 70 (2024).","mla":"Browning, Timothy D., and Matteo Verzobio. “Strong Divisibility Sequences and Sieve Methods.” <i>Mathematika</i>, vol. 70, no. 4, e12269, London Mathematical Society, 2024, doi:<a href=\"https://doi.org/10.1112/mtk.12269\">10.1112/mtk.12269</a>.","ieee":"T. D. Browning and M. Verzobio, “Strong divisibility sequences and sieve methods,” <i>Mathematika</i>, vol. 70, no. 4. London Mathematical Society, 2024.","apa":"Browning, T. D., &#38; Verzobio, M. (2024). Strong divisibility sequences and sieve methods. <i>Mathematika</i>. London Mathematical Society. <a href=\"https://doi.org/10.1112/mtk.12269\">https://doi.org/10.1112/mtk.12269</a>","ama":"Browning TD, Verzobio M. Strong divisibility sequences and sieve methods. <i>Mathematika</i>. 2024;70(4). doi:<a href=\"https://doi.org/10.1112/mtk.12269\">10.1112/mtk.12269</a>"},"language":[{"iso":"eng"}],"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.","abstract":[{"lang":"eng","text":"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."}],"ddc":["510"],"oa_version":"Published Version","issue":"4","author":[{"first_name":"Timothy D","full_name":"Browning, Timothy D","orcid":"0000-0002-8314-0177","last_name":"Browning","id":"35827D50-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Verzobio","id":"7aa8f170-131e-11ed-88e1-a9efd01027cb","full_name":"Verzobio, Matteo","first_name":"Matteo","orcid":"0000-0002-0854-0306"}],"_id":"17323","department":[{"_id":"TiBr"}],"status":"public","type":"journal_article","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_number":"e12269","publication_identifier":{"issn":["0025-5793"],"eissn":["2041-7942"]},"publication_status":"published","oa":1,"date_updated":"2024-07-29T11:28:47Z","intvolume":"        70","month":"07","project":[{"grant_number":"P36278","name":"Rational curves via function field analytic number theory","_id":"bd8a4fdc-d553-11ed-ba76-80a0167441a3"},{"_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","name":"IST-BRIDGE: International postdoctoral program","call_identifier":"H2020","grant_number":"101034413"}],"date_created":"2024-07-28T22:01:08Z","year":"2024","publication":"Mathematika","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"day":"23","doi":"10.1112/mtk.12269","has_accepted_license":"1"}