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Mathematics of Computation

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Computing totally positive algebraic integers of small trace

Author: James McKee
Journal: Math. Comp. 80 (2011), 1041-1052
MSC (2010): Primary 11R04, 11Y40
Published electronically: October 22, 2010
Table supplement: Some minimal trace totally positive algebraic integers (PDF)
MathSciNet review: 2772109
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Abstract: We construct minimal polynomials of totally positive algebraic integers of small absolute trace by consideration of their reductions modulo auxiliary polynomials. Many new examples of such polynomials of minimal absolute trace (for given degree) are found. The computations are pushed to degrees that previously were unattainable, and one consequence is that the new examples form the majority of all those known. As an application, we produce a new bound for the Schur-Siegel-Smyth trace problem.

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Additional Information

James McKee
Affiliation: Department of Mathematics, Royal Holloway, University of London, Egham Hill, Egham, Surrey, TW20 0EX, England, United Kingdom

Received by editor(s): December 23, 2009
Received by editor(s) in revised form: February 22, 2010
Published electronically: October 22, 2010
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.