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

 

Two new points in the spectrum of the absolute Mahler measure
of totally positive algebraic integers


Author: V. Flammang
Journal: Math. Comp. 65 (1996), 307-311
MSC (1991): Primary 11R06, 11J68
MathSciNet review: 1320894
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Abstract: For totally positive algebraic integers $\alpha \ne 0,1$ of degree $d(\alpha )$, we consider the set $\mathcal{L}$ of values of $M(\alpha )^{\frac{1}{d(\alpha )}}=\Omega (\alpha )$, where $M(\alpha )$ is the Mahler measure of $\alpha $. C. J. Smyth has found the four smallest values of $\mathcal{L}$ and conjectured that the fifth point is $\Omega ((2\cos \frac{2\pi }{60})^2)$. We prove that this is so and, moreover, we give the sixth point of $\mathcal{L}$.


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Additional Information

V. Flammang
Affiliation: address URA CNRS n$^{\roman}o$ 399, Département de Mathématiques et Informatique, U.F.R. MIM. Université de Metz, Ile du Saulcy, 57045 Metz, Cedex 1, France
Email: flammang@poncelet.univ-metz.fr

DOI: http://dx.doi.org/10.1090/S0025-5718-96-00664-3
PII: S 0025-5718(96)00664-3
Received by editor(s): February 1, 1994
Article copyright: © Copyright 1996 American Mathematical Society