{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T07:50:28Z","timestamp":1776844228873,"version":"3.51.2"},"reference-count":12,"publisher":"American Mathematical Society (AMS)","issue":"266","license":[{"start":{"date-parts":[[2009,9,8]],"date-time":"2009-09-08T00:00:00Z","timestamp":1252368000000},"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>Explicit auxiliary functions can be used in the \u201cSchur-Siegel- Smyth trace problem\u201d. In the previous works, these functions were constructed only with polynomials having all their roots positive. Here, we use several polynomials with complex roots, which are found with Wu\u2019s algorithm, and we improve the known lower bounds for the absolute trace of totally positive algebraic integers. This improvement has a consequence for the search of Salem numbers that have a negative trace. The same method also gives a small improvement of the upper bound for the integer transfinite diameter of [0,1].<\/p>","DOI":"10.1090\/s0025-5718-08-02120-0","type":"journal-article","created":{"date-parts":[[2009,12,1]],"date-time":"2009-12-01T13:09:23Z","timestamp":1259672963000},"page":"1119-1125","source":"Crossref","is-referenced-by-count":29,"title":["Trace of totally positive algebraic integers and integer transfinite diameter"],"prefix":"10.1090","volume":"78","author":[{"given":"V.","family":"Flammang","sequence":"first","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2008,9,8]]},"reference":[{"key":"1","unstructured":"[AP] J. Aguirre and J.C. Peral. The trace problem for totally positive algebraic integers, Number Theory and Polynomials. (Conference proceedings, University of Bristol, 3-7 April 2006, editors J.F. McKee and C.J. Smyth). LMS Lecture notes."},{"key":"2","series-title":"CMS Books in Mathematics\/Ouvrages de Math\\'{e}matiques de la SMC","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-21652-2","volume-title":"Computational excursions in analysis and number theory","volume":"10","author":"Borwein, Peter","year":"2002","ISBN":"https:\/\/id.crossref.org\/isbn\/0387954449"},{"issue":"3","key":"3","doi-asserted-by":"publisher","first-page":"779","DOI":"10.5802\/aif.1473","article-title":"Sur le diam\u00e8tre transfini entier d\u2019un intervalle \u00e0 extr\u00e9mit\u00e9s rationnelles","volume":"45","author":"Flammang, Val\u00e9rie","year":"1995","journal-title":"Ann. Inst. 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