{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,16]],"date-time":"2023-10-16T15:55:09Z","timestamp":1697471709194},"reference-count":1,"publisher":"Cambridge University Press (CUP)","issue":"6","license":[{"start":{"date-parts":[[2021,4,8]],"date-time":"2021-04-08T00:00:00Z","timestamp":1617840000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2021,11]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We prove that if <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548321000092_inline1.png\" \/><jats:tex-math>\n$A \\subseteq [X,\\,2X]$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> and <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548321000092_inline2.png\" \/><jats:tex-math>\n$B \\subseteq [Y,\\,2Y]$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> are sets of integers such that gcd (<jats:italic>a, b<\/jats:italic>) \u2a7e <jats:italic>D<\/jats:italic> for at least \u03b4|A||B| pairs (<jats:italic>a, b<\/jats:italic>) <jats:italic>\u03b5 A<\/jats:italic> \u00d7 <jats:italic>B<\/jats:italic> then <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548321000092_inline3.png\" \/><jats:tex-math>\n$|A||B|{ \\ll _{\\rm{\\varepsilon }}}{\\delta ^{ - 2 - \\varepsilon }}XY\/{D^2}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>. This is a new result even when \u03b4 = 1. The proof uses ideas of Koukoulopoulos and Maynard and some additional combinatorial arguments.<\/jats:p>","DOI":"10.1017\/s0963548321000092","type":"journal-article","created":{"date-parts":[[2021,4,8]],"date-time":"2021-04-08T08:43:27Z","timestamp":1617871407000},"page":"922-929","update-policy":"http:\/\/dx.doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":1,"title":["Extremal problems for GCDs"],"prefix":"10.1017","volume":"30","author":[{"given":"Ben","family":"Green","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Aled","family":"Walker","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2021,4,8]]},"reference":[{"key":"S0963548321000092_ref1","doi-asserted-by":"publisher","DOI":"10.4007\/annals.2020.192.1.5"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548321000092","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,10,15]],"date-time":"2021-10-15T15:51:35Z","timestamp":1634313095000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548321000092\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,4,8]]},"references-count":1,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2021,11]]}},"alternative-id":["S0963548321000092"],"URL":"https:\/\/doi.org\/10.1017\/s0963548321000092","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,4,8]]},"assertion":[{"value":"\u00a9 The Author(s), 2021. Published by Cambridge University Press","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http:\/\/creativecommons.org\/licenses\/by\/4.0\/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.","name":"license","label":"License","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}