The trace of totally positive algebraic integers
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- by Julián Aguirre, Mikel Bilbao and Juan Carlos Peral;
- Math. Comp. 75 (2006), 385-393
- DOI: https://doi.org/10.1090/S0025-5718-05-01776-X
- Published electronically: September 12, 2005
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Abstract:
For all totally positive algebraic numbers $\alpha$ except a finite number of explicit exceptions, the following inequality holds: \[ \frac {1}{d} (\alpha _1+\dots +\alpha _d)>\max (1.780022,1.66+\alpha _1), \] 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.References
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Bibliographic 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
- MR Author ID: 137825
- Email: mtppealj@lg.ehu.es
- Received by editor(s): July 2, 2004
- Received by editor(s) in revised form: October 27, 2004
- Published electronically: September 12, 2005
- © Copyright 2005 American Mathematical Society
- Journal: Math. Comp. 75 (2006), 385-393
- MSC (2000): Primary 11R06, 11-04
- DOI: https://doi.org/10.1090/S0025-5718-05-01776-X
- MathSciNet review: 2176405