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Trace of totally positive algebraic integers and integer transfinite diameter


Author: V. Flammang
Journal: Math. Comp. 78 (2009), 1119-1125
MSC (2000): Primary 11R04, 11Y40
DOI: https://doi.org/10.1090/S0025-5718-08-02120-0
Published electronically: September 8, 2008
MathSciNet review: 2476574
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Abstract: Explicit auxiliary functions can be used in the ``Schur-Siegel- Smyth trace problem''. 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's 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].


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Additional Information

V. Flammang
Affiliation: UMR CNRS 7122 Département de Mathématiques, UFR MIM, Université Paul Verlaine de Metz, Ile du Saulcy, 57045 METZ cedex 01, France
Email: flammang@univ-metz.fr

DOI: https://doi.org/10.1090/S0025-5718-08-02120-0
Received by editor(s): April 2, 2007
Received by editor(s) in revised form: June 22, 2007
Published electronically: September 8, 2008
Article copyright: © Copyright 2008 American Mathematical Society

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