{"quality_controlled":"1","has_accepted_license":"1","department":[{"_id":"TiBr"}],"scopus_import":"1","ddc":["510"],"abstract":[{"lang":"eng","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."}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2025-01-14T06:53:11Z","doi":"10.1112/mtk.70008","year":"2025","publisher":"London Mathematical Society","project":[{"call_identifier":"H2020","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","grant_number":"101034413","name":"IST-BRIDGE: International postdoctoral program"}],"article_processing_charge":"Yes (via OA deal)","tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"_id":"18822","day":"02","article_number":"e70008","publication_status":"published","type":"journal_article","title":"Diagonal cubic forms and the large sieve","oa_version":"Published Version","ec_funded":1,"month":"01","status":"public","volume":71,"publication_identifier":{"issn":["0025-5793"],"eissn":["2041-7942"]},"oa":1,"date_published":"2025-01-02T00:00:00Z","file_date_updated":"2025-01-14T06:52:09Z","citation":{"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>.","ista":"Wang V. 2025. Diagonal cubic forms and the large sieve. Mathematika. 71(1), e70008.","ieee":"V. Wang, “Diagonal cubic forms and the large sieve,” <i>Mathematika</i>, vol. 71, no. 1. London Mathematical Society, 2025.","short":"V. Wang, Mathematika 71 (2025).","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>.","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>"},"corr_author":"1","date_created":"2025-01-12T23:04:01Z","issue":"1","language":[{"iso":"eng"}],"publication":"Mathematika","intvolume":"        71","OA_type":"hybrid","article_type":"original","file":[{"relation":"main_file","access_level":"open_access","content_type":"application/pdf","success":1,"date_updated":"2025-01-14T06:52:09Z","file_id":"18845","checksum":"700a8596b4bffce2320d074120962c22","file_size":309893,"creator":"dernst","file_name":"2025_Mathematika_Wang.pdf","date_created":"2025-01-14T06:52:09Z"}],"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.","OA_place":"publisher","author":[{"orcid":"0000-0002-0704-7026","full_name":"Wang, Victor","first_name":"Victor","last_name":"Wang","id":"76096395-aea4-11ed-a680-ab8ebbd3f1b9"}]}