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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

The trace of totally positive algebraic integers


Authors: Julián Aguirre, Mikel Bilbao and Juan Carlos Peral
Journal: Math. Comp. 75 (2006), 385-393
MSC (2000): Primary 11R06, 11-04
Published electronically: September 12, 2005
MathSciNet review: 2176405
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Abstract | References | Similar Articles | Additional Information

Abstract: For all totally positive algebraic numbers $\alpha$ except a finite number of explicit exceptions, the following inequality holds:

\begin{displaymath}\frac{1}{d}\,(\alpha_1+\dots+\alpha_d)>\max(1.780022,1.66+\alpha_1), \end{displaymath}

where $d$ is the degree of $\alpha$ and $0<\alpha_1<\dots<\alpha_d$ its conjugates. This improves previous results of Smyth, Flammang and Rhin.


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Additional Information

Julián Aguirre
Affiliation: Departamento de Matemáticas, Universidad del País Vasco, Aptdo. 644, 48080 Bilbao, Spain
Email: mtpagesj@lg.ehu.es

Mikel Bilbao
Affiliation: Departamento de Economía Aplicada I, Universidad del País Vasco, Avda. Lehendakari Aguirre 83, 48015 Bilbao, Spain
Email: elpbillm@bs.ehu.es

Juan Carlos Peral
Affiliation: Departamento de Matemáticas, Universidad del País Vasco, Aptdo. 644, 48080 Bilbao, Spain
Email: mtppealj@lg.ehu.es

DOI: http://dx.doi.org/10.1090/S0025-5718-05-01776-X
PII: S 0025-5718(05)01776-X
Received by editor(s): July 2, 2004
Received by editor(s) in revised form: October 27, 2004
Published electronically: September 12, 2005
Article copyright: © Copyright 2005 American Mathematical Society