[{"has_accepted_license":"1","status":"public","corr_author":"1","publisher":"London Mathematical Society","publication":"Mathematika","OA_place":"publisher","publication_identifier":{"eissn":["2041-7942"],"issn":["0025-5793"]},"month":"01","intvolume":"        71","acknowledgement":"I thank Peter Sarnak for suggesting projects that ultimately led to the present paper. I also thank him for many encouraging discussions, helpful comments, and references. Thanks also to Tim Browning, Trevor Wooley, and Nina Zubrilina for helpful comments, and to Levent Alpöge and Will Sawin for some interesting old discussions. I thank Yang Liu, Evan O'Dorney, Ashwin Sah, and Mark Sellke for conversations illuminating the combinatorics of an older, counting version of the present Lemma 4.9. Finally, special thanks are due to the editors and referees for their patience and help with the exposition. This work was partially supported by NSF Grant DMS-1802211, and the European Union's Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant Agreement No. 101034413.","author":[{"id":"76096395-aea4-11ed-a680-ab8ebbd3f1b9","orcid":"0000-0002-0704-7026","first_name":"Victor","full_name":"Wang, Victor","last_name":"Wang"}],"article_number":"e70008","ddc":["510"],"external_id":{"isi":["001388255500001"]},"year":"2025","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","volume":71,"date_published":"2025-01-02T00:00:00Z","oa_version":"Published Version","article_processing_charge":"Yes (via OA deal)","title":"Diagonal cubic forms and the large sieve","OA_type":"hybrid","scopus_import":"1","ec_funded":1,"abstract":[{"text":"Let N(X) be the number of integral zeros (mathematical equation). Works of Hooley and Heath-Brown imply (mathematical equation), if one assumes automorphy and grand Riemann hypothesis for certain Hasse–Weil L-functions. Assuming instead a natural large sieve inequality, we recover the same bound on N(X). This is part of a more general statement, for diagonal cubic forms in (mathematical equation) variables, where we allow approximations to Hasse–Weil L-functions.","lang":"eng"}],"oa":1,"file_date_updated":"2025-01-14T06:52:09Z","language":[{"iso":"eng"}],"citation":{"ista":"Wang V. 2025. Diagonal cubic forms and the large sieve. Mathematika. 71(1), e70008.","apa":"Wang, V. (2025). Diagonal cubic forms and the large sieve. <i>Mathematika</i>. London Mathematical Society. <a href=\"https://doi.org/10.1112/mtk.70008\">https://doi.org/10.1112/mtk.70008</a>","ama":"Wang V. Diagonal cubic forms and the large sieve. <i>Mathematika</i>. 2025;71(1). doi:<a href=\"https://doi.org/10.1112/mtk.70008\">10.1112/mtk.70008</a>","mla":"Wang, Victor. “Diagonal Cubic Forms and the Large Sieve.” <i>Mathematika</i>, vol. 71, no. 1, e70008, London Mathematical Society, 2025, doi:<a href=\"https://doi.org/10.1112/mtk.70008\">10.1112/mtk.70008</a>.","ieee":"V. Wang, “Diagonal cubic forms and the large sieve,” <i>Mathematika</i>, vol. 71, no. 1. London Mathematical Society, 2025.","chicago":"Wang, Victor. “Diagonal Cubic Forms and the Large Sieve.” <i>Mathematika</i>. London Mathematical Society, 2025. <a href=\"https://doi.org/10.1112/mtk.70008\">https://doi.org/10.1112/mtk.70008</a>.","short":"V. Wang, Mathematika 71 (2025)."},"date_updated":"2025-04-14T07:54:56Z","quality_controlled":"1","_id":"18822","issue":"1","date_created":"2025-01-12T23:04:01Z","publication_status":"published","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"type":"journal_article","department":[{"_id":"TiBr"}],"doi":"10.1112/mtk.70008","file":[{"content_type":"application/pdf","checksum":"700a8596b4bffce2320d074120962c22","access_level":"open_access","success":1,"date_updated":"2025-01-14T06:52:09Z","file_name":"2025_Mathematika_Wang.pdf","file_id":"18845","relation":"main_file","creator":"dernst","date_created":"2025-01-14T06:52:09Z","file_size":309893}],"article_type":"original","isi":1,"day":"02","project":[{"name":"IST-BRIDGE: International postdoctoral program","grant_number":"101034413","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","call_identifier":"H2020"}]},{"publication_identifier":{"issn":["0025-5793"],"eissn":["2041-7942"]},"intvolume":"        70","month":"10","corr_author":"1","status":"public","has_accepted_license":"1","OA_place":"publisher","publication":"Mathematika","publisher":"London Mathematical Society","volume":70,"date_published":"2024-10-01T00:00:00Z","oa_version":"Published Version","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","year":"2024","title":"Strong divisibility sequences and sieve methods","article_processing_charge":"Yes (via OA deal)","author":[{"orcid":"0000-0002-8314-0177","id":"35827D50-F248-11E8-B48F-1D18A9856A87","last_name":"Browning","full_name":"Browning, Timothy D","first_name":"Timothy D"},{"orcid":"0000-0002-0854-0306","id":"7aa8f170-131e-11ed-88e1-a9efd01027cb","last_name":"Verzobio","first_name":"Matteo","full_name":"Verzobio, Matteo"}],"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.","external_id":{"isi":["001273912800001"]},"ddc":["510"],"article_number":"e12269","quality_controlled":"1","date_updated":"2025-09-08T08:44:11Z","citation":{"ista":"Browning TD, Verzobio M. 2024. Strong divisibility sequences and sieve methods. Mathematika. 70(4), e12269.","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>","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.","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>.","short":"T.D. Browning, M. Verzobio, Mathematika 70 (2024)."},"_id":"17323","issue":"4","scopus_import":"1","OA_type":"hybrid","language":[{"iso":"eng"}],"file_date_updated":"2025-01-13T11:06:25Z","oa":1,"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."}],"ec_funded":1,"article_type":"original","project":[{"grant_number":"P36278","name":"Rational curves via function field analytic number theory","_id":"bd8a4fdc-d553-11ed-ba76-80a0167441a3"},{"name":"IST-BRIDGE: International postdoctoral program","grant_number":"101034413","call_identifier":"H2020","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c"}],"isi":1,"day":"01","type":"journal_article","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"publication_status":"published","date_created":"2024-07-28T22:01:08Z","file":[{"content_type":"application/pdf","file_name":"2024_Mathematika_Browning.pdf","date_updated":"2025-01-13T11:06:25Z","success":1,"access_level":"open_access","checksum":"0b1518bdc1a901413005c19202cfa497","relation":"main_file","file_id":"18842","file_size":273006,"date_created":"2025-01-13T11:06:25Z","creator":"dernst"}],"department":[{"_id":"TiBr"}],"doi":"10.1112/mtk.12269"}]