{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T20:07:24Z","timestamp":1776802044802,"version":"3.51.2"},"reference-count":24,"publisher":"American Mathematical Society (AMS)","issue":"302","license":[{"start":{"date-parts":[[2017,3,2]],"date-time":"2017-03-02T00:00:00Z","timestamp":1488412800000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/100006462","name":"City University of New York","doi-asserted-by":"publisher","award":["PSC CUNY #65644-00 34"],"award-info":[{"award-number":["PSC CUNY #65644-00 34"]}],"id":[{"id":"10.13039\/100006462","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>We show that the dilogarithm has at most one zero on each branch, that each zero is close to a root of unity, and that they may be found to any precision with Newton\u2019s method. This work is motivated by applications to the asymptotics of coefficients in partial fraction decompositions considered by Rademacher. We also survey what is known about zeros of polylogarithms in general.<\/p>","DOI":"10.1090\/mcom\/3065","type":"journal-article","created":{"date-parts":[[2015,4,8]],"date-time":"2015-04-08T11:03:24Z","timestamp":1428491004000},"page":"2967-2993","source":"Crossref","is-referenced-by-count":3,"title":["Zeros of the dilogarithm"],"prefix":"10.1090","volume":"85","author":[{"given":"Cormac","family":"O\u2019Sullivan","sequence":"first","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2016,3,2]]},"reference":[{"key":"1","series-title":"Encyclopedia of Mathematics and its Applications","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781107325937","volume-title":"Special functions","volume":"71","author":"Andrews, George E.","year":"1999","ISBN":"https:\/\/id.crossref.org\/isbn\/0521623219"},{"key":"2","series-title":"Discrete Mathematics and its Applications (Boca Raton)","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1201\/b12210","volume-title":"Combinatorics of permutations","author":"B\u00f3na, Mikl\u00f3s","year":"2012","ISBN":"https:\/\/id.crossref.org\/isbn\/9781439850510","edition":"2"},{"key":"3","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1090\/S2330-1511-2014-00014-6","article-title":"Disproof of a conjecture by Rademacher on partial fractions","volume":"1","author":"Drmota, Michael","year":"2014","journal-title":"Proc. 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O\u2019Sullivan, Asymptotics for the partial fractions of the restricted partition generating function I. arXiv:1507.07975."},{"key":"13","unstructured":"[O\u2019Sb] C. O\u2019Sullivan , Asymptotics for the partial fractions of the restricted partition generating function II. arXiv:1507.07977."},{"issue":"2","key":"14","doi-asserted-by":"publisher","first-page":"735","DOI":"10.1515\/forum-2012-0073","article-title":"On the partial fraction decomposition of the restricted partition generating function","volume":"27","author":"O\u2019Sullivan, Cormac","year":"2015","journal-title":"Forum Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0933-7741","issn-type":"print"},{"key":"15","first-page":"193","article-title":"On the zeros of power series","volume":"13","author":"Peyerimhoff, Alexander","year":"1966","journal-title":"Michigan Math. 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