{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,21]],"date-time":"2026-05-21T00:14:08Z","timestamp":1779322448043,"version":"3.51.4"},"reference-count":10,"publisher":"American Mathematical Society (AMS)","issue":"285","license":[{"start":{"date-parts":[[2014,5,28]],"date-time":"2014-05-28T00:00:00Z","timestamp":1401235200000},"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>In this article, we study the Mertens conjecture. We revisit and improve the original constructive disproof of J\u00e1nos Pintz. We obtain a new lower bound for the minimal counterexample and new numerical results for this conjecture.<\/p>","DOI":"10.1090\/s0025-5718-2013-02716-0","type":"journal-article","created":{"date-parts":[[2013,5,28]],"date-time":"2013-05-28T11:35:52Z","timestamp":1369740952000},"page":"421-433","source":"Crossref","is-referenced-by-count":4,"title":["Improved results on the Mertens conjecture"],"prefix":"10.1090","volume":"83","author":[{"given":"Yannick","family":"Saouter","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Herman","family":"Riele","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2013,5,28]]},"reference":[{"issue":"1940","key":"1","doi-asserted-by":"publisher","first-page":"477","DOI":"10.1098\/rspa.1995.0096","article-title":"The Riemann zeta-function and its derivatives","volume":"450","author":"Choudhury, Bejoy K.","year":"1995","journal-title":"Proc. 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(2)","ISSN":"https:\/\/id.crossref.org\/issn\/0024-6107","issn-type":"print"},{"key":"4","isbn-type":"print","doi-asserted-by":"publisher","first-page":"156","DOI":"10.1007\/11792086_12","article-title":"The Mertens conjecture revisited","author":"Kotnik, Tadej","year":"2006","ISBN":"https:\/\/id.crossref.org\/isbn\/9783540360759"},{"issue":"4","key":"5","doi-asserted-by":"publisher","first-page":"515","DOI":"10.1007\/BF01457454","article-title":"Factoring polynomials with rational coefficients","volume":"261","author":"Lenstra, A. K.","year":"1982","journal-title":"Math. Ann.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5831","issn-type":"print"},{"key":"6","unstructured":"[Mer97] F. Mertens. \u00dcber eine zahlentheoretische Funktion. Sitzungberichte Akad. Wiss. Wien IIa, (106), 1897."},{"key":"7","doi-asserted-by":"publisher","first-page":"138","DOI":"10.1515\/crll.1985.357.138","article-title":"Disproof of the Mertens conjecture","volume":"357","author":"Odlyzko, A. 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