{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,25]],"date-time":"2025-02-25T05:29:08Z","timestamp":1740461348035,"version":"3.37.3"},"reference-count":12,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2024,11,21]],"date-time":"2024-11-21T00:00:00Z","timestamp":1732147200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2025,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We prove that any increasing sequence of real numbers with average gap <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548324000361_inline1.png\"\/><jats:tex-math>\n$1$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> and Poisson pair correlations has some gap that is at least <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548324000361_inline2.png\"\/><jats:tex-math>\n$3\/2+10^{-9}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>. This improves upon a result of Aistleitner, Blomer, and Radziwi\u0142\u0142.<\/jats:p>","DOI":"10.1017\/s0963548324000361","type":"journal-article","created":{"date-parts":[[2024,11,21]],"date-time":"2024-11-21T06:46:56Z","timestamp":1732171616000},"page":"283-297","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":0,"title":["On the smallest gap in a sequence with Poisson pair correlations"],"prefix":"10.1017","volume":"34","author":[{"given":"Daniel","family":"Altman","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zachary","family":"Chase","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2024,11,21]]},"reference":[{"key":"S0963548324000361_ref12","doi-asserted-by":"publisher","DOI":"10.1016\/j.indag.2018.04.001"},{"key":"S0963548324000361_ref9","doi-asserted-by":"publisher","DOI":"10.4064\/aa-89-3-283-293"},{"volume-title":"Uniform distribution of sequences","year":"2006","author":"Kuipers","key":"S0963548324000361_ref7"},{"key":"S0963548324000361_ref4","doi-asserted-by":"publisher","DOI":"10.4007\/annals.2005.161.679"},{"key":"S0963548324000361_ref6","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004109990466"},{"key":"S0963548324000361_ref1","doi-asserted-by":"publisher","DOI":"10.4171\/jems\/1356"},{"key":"S0963548324000361_ref3","doi-asserted-by":"publisher","DOI":"10.1007\/s11856-017-1597-5"},{"key":"S0963548324000361_ref8","doi-asserted-by":"publisher","DOI":"10.1007\/s002200050348"},{"key":"S0963548324000361_ref11","unstructured":"[10] Sarnak, P. (1997) Values at integers of binary quadratic forms. Harmonic analysis and number theory (Montreal 1996), 181-203, CMS Conf. Providence, RI.: Amer. Math. Soc., Proc. 21."},{"key":"S0963548324000361_ref13","doi-asserted-by":"publisher","DOI":"10.1112\/S002557931700050X"},{"key":"S0963548324000361_ref10","doi-asserted-by":"publisher","DOI":"10.1515\/form.2002.030"},{"key":"S0963548324000361_ref2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jnt.2017.06.009"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548324000361","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,24]],"date-time":"2025-02-24T12:38:42Z","timestamp":1740400722000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548324000361\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,11,21]]},"references-count":12,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2025,3]]}},"alternative-id":["S0963548324000361"],"URL":"https:\/\/doi.org\/10.1017\/s0963548324000361","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"type":"print","value":"0963-5483"},{"type":"electronic","value":"1469-2163"}],"subject":[],"published":{"date-parts":[[2024,11,21]]},"assertion":[{"value":"\u00a9 The Author(s), 2024. Published by Cambridge University Press","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}}]}}