{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T07:42:09Z","timestamp":1776843729755,"version":"3.51.2"},"reference-count":14,"publisher":"American Mathematical Society (AMS)","issue":"224","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"

\n We describe several searches for polynomials with integer coefficients and small Mahler measure. We describe the algorithm used to test Mahler measures. We determine all polynomials with degree at most 24 and Mahler measure less than\n \n \n \n 1.3<\/mml:mn>\n 1.3<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n , test all reciprocal and antireciprocal polynomials with height\u00a01 and degree at most 40, and check certain sparse polynomials with height\u00a01 and degree as large as 181. We find a new limit point of Mahler measures near\n \n \n \n 1.309<\/mml:mn>\n 1.309<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n , four new Salem numbers less than\n \n \n \n 1.3<\/mml:mn>\n 1.3<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n , and many new polynomials with small Mahler measure. None has measure smaller than that of Lehmer\u2019s degree 10 polynomial.\n <\/p>","DOI":"10.1090\/s0025-5718-98-01006-0","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:14:44Z","timestamp":1027707284000},"page":"1697-1705","source":"Crossref","is-referenced-by-count":29,"title":["Polynomials with small Mahler measure"],"prefix":"10.1090","volume":"67","author":[{"given":"Michael","family":"Mossinghoff","sequence":"first","affiliation":[]}],"member":"14","published-online":{"date-parts":[[1998]]},"reference":[{"key":"1","isbn-type":"print","first-page":"53","article-title":"Polynomials with low height and prescribed vanishing","author":"Bombieri, Enrico","year":"1987","ISBN":"https:\/\/id.crossref.org\/isbn\/0817633618"},{"key":"2","doi-asserted-by":"publisher","first-page":"188","DOI":"10.1049\/el:19710125","article-title":"Realisation from partial sequences","volume":"7","author":"Hiller, J.","year":"1971","journal-title":"Electron. Lett.","ISSN":"https:\/\/id.crossref.org\/issn\/0013-5194","issn-type":"print"},{"issue":"144","key":"3","doi-asserted-by":"publisher","first-page":"1244","DOI":"10.2307\/2006349","article-title":"Pisot and Salem numbers in intervals of the real line","volume":"32","author":"Boyd, David W.","year":"1978","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"152","key":"4","doi-asserted-by":"publisher","first-page":"1361","DOI":"10.2307\/2006402","article-title":"Reciprocal polynomials having small measure","volume":"35","author":"Boyd, David W.","year":"1980","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"4","key":"5","doi-asserted-by":"publisher","first-page":"453","DOI":"10.4153\/CMB-1981-069-5","article-title":"Speculations concerning the range of Mahler\u2019s measure","volume":"24","author":"Boyd, David W.","year":"1981","journal-title":"Canad. Math. Bull.","ISSN":"https:\/\/id.crossref.org\/issn\/0008-4395","issn-type":"print"},{"issue":"187","key":"6","doi-asserted-by":"publisher","first-page":"355","DOI":"10.2307\/2008368","article-title":"Reciprocal polynomials having small measure. II","volume":"53","author":"Boyd, David W.","year":"1989","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"4","key":"7","doi-asserted-by":"publisher","first-page":"391","DOI":"10.4064\/aa-34-4-391-401","article-title":"On a question of Lehmer and the number of irreducible factors of a polynomial","volume":"34","author":"Dobrowolski, E.","year":"1979","journal-title":"Acta Arith.","ISSN":"https:\/\/id.crossref.org\/issn\/0065-1036","issn-type":"print"},{"key":"8","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1007\/BF02547750","article-title":"The method of successive approximations for functional equations","volume":"71","author":"Kantorovitch, L.","year":"1939","journal-title":"Acta Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0001-5962","issn-type":"print"},{"key":"9","doi-asserted-by":"crossref","unstructured":"D. H. Lehmer, Factorization of certain cyclotomic functions, Ann. of Math. (2) 34 (1933), 461\u2013479.","DOI":"10.2307\/1968172"},{"key":"10","unstructured":"M. J. Mossinghoff, Algorithms for the determination of polynomials with small Mahler measure, Ph.D. Thesis, The University of Texas at Austin, 1995."},{"key":"11","doi-asserted-by":"crossref","unstructured":"M. J. Mossinghoff, C. G. Pinner, and J. D. Vaaler, Perturbing polynomials with all their roots on the unit circle, Math. Comp. 67 (1998), 1707\u20131726.","DOI":"10.1090\/S0025-5718-98-01007-2"},{"key":"12","series-title":"Proceedings of Symposia in Applied Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1090\/psapm\/048","volume-title":"Mathematics of Computation 1943--1993: a half-century of computational mathematics","volume":"48","year":"1994","ISBN":"https:\/\/id.crossref.org\/isbn\/0821802917"},{"key":"13","doi-asserted-by":"publisher","first-page":"169","DOI":"10.1112\/blms\/3.2.169","article-title":"On the product of the conjugates outside the unit circle of an algebraic integer","volume":"3","author":"Smyth, C. J.","year":"1971","journal-title":"Bull. London Math. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0024-6093","issn-type":"print"},{"key":"14","isbn-type":"print","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-5592-3","volume-title":"Introduction to numerical analysis","author":"Stoer, J.","year":"1980","ISBN":"https:\/\/id.crossref.org\/isbn\/0387904204"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/1998-67-224\/S0025-5718-98-01006-0\/S0025-5718-98-01006-0.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/1998-67-224\/S0025-5718-98-01006-0\/S0025-5718-98-01006-0.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T21:52:03Z","timestamp":1776721923000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/1998-67-224\/S0025-5718-98-01006-0\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998]]},"references-count":14,"journal-issue":{"issue":"224","published-print":{"date-parts":[[1998,10]]}},"alternative-id":["S0025-5718-98-01006-0"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-98-01006-0","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[1998]]}}}