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On the absolute Mahler measure of polynomials having all zeros in a sector. II


Authors: Georges Rhin and Qiang Wu
Journal: Math. Comp. 74 (2005), 383-388
MSC (2000): Primary 11R04, 12D10
Published electronically: May 21, 2004
MathSciNet review: 2085898
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $\alpha $ be an algebraic integer of degree $d$, not $0$ or a root of unity, all of whose conjugates $\alpha _{i}$ are confined to a sector $\vert \operatorname{arg} z \vert \le \theta $. In the paper On the absolute Mahler measure of polynomials having all zeros in a sector, G. Rhin and C. Smyth compute the greatest lower bound $c(\theta )$ of the absolute Mahler measure ( $\prod _{i=1}^{d} \max (1, \vert \alpha _{i} \vert ))^{1/d}$ of $\alpha $, for $\theta $ belonging to nine subintervals of $[0, 2\pi /3]$. In this paper, we improve the result to thirteen subintervals of $[0,\pi ]$ and extend some existing subintervals.


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Additional Information

Georges Rhin
Affiliation: Laboratoire MMAS, CNRS UMR 7122, Université de Metz, Ile du Saulcy, 57045 METZ Cedex 1, France
Email: rhin@poncelet.univ-metz.fr

Qiang Wu
Affiliation: Laboratoire MMAS, CNRS UMR 7122, Université de Metz, Ile du Saulcy, 57045 METZ Cedex 1, France
Email: wu@poncelet.univ-metz.fr

DOI: https://doi.org/10.1090/S0025-5718-04-01676-X
Received by editor(s): March 12, 2003
Received by editor(s) in revised form: August 10, 2003
Published electronically: May 21, 2004
Article copyright: © Copyright 2004 American Mathematical Society