{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T22:46:12Z","timestamp":1776725172044,"version":"3.51.2"},"reference-count":21,"publisher":"American Mathematical Society (AMS)","issue":"233","license":[{"start":{"date-parts":[[2001,6,12]],"date-time":"2001-06-12T00:00:00Z","timestamp":992304000000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>A refined version of Manin\u2019s conjecture about the asymptotics of points of bounded height on Fano varieties has been developed by Batyrev and the authors. We test numerically this refined conjecture for some diagonal cubic surfaces.<\/p>","DOI":"10.1090\/s0025-5718-00-01189-3","type":"journal-article","created":{"date-parts":[[2005,7,11]],"date-time":"2005-07-11T17:02:26Z","timestamp":1121101346000},"page":"367-387","source":"Crossref","is-referenced-by-count":19,"title":["Tamagawa numbers of diagonal cubic surfaces, numerical evidence"],"prefix":"10.1090","volume":"70","author":[{"given":"Emmanuel","family":"Peyre","sequence":"first","affiliation":[]},{"given":"Yuri","family":"Tschinkel","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2000,6,12]]},"reference":[{"issue":"1-3","key":"1","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1007\/BF01453564","article-title":"Sur le nombre des points rationnels de hauteur born\u00e9 des vari\u00e9t\u00e9s alg\u00e9briques","volume":"286","author":"Batyrev, V. V.","year":"1990","journal-title":"Math. 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Bernstein, Enumerating solutions to \ud835\udc5d(\ud835\udc4e)+\ud835\udc5e(\ud835\udc4f)=\ud835\udc5f(\ud835\udc50)+\ud835\udc60(\ud835\udc51), Preprint (1998)."},{"key":"6","series-title":"Graduate Texts in Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-02945-9","volume-title":"A course in computational algebraic number theory","volume":"138","author":"Cohen, Henri","year":"1993","ISBN":"https:\/\/id.crossref.org\/isbn\/3540556400"},{"issue":"1","key":"7","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/BF01393336","article-title":"Hilbert\u2019s Theorem 90 for \ud835\udc3e\u2082, with application to the Chow groups of rational surfaces","volume":"71","author":"Colliot-Th\u00e9l\u00e8ne, Jean-Louis","year":"1983","journal-title":"Invent. 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