Integer transfinite diameter and polynomials with small Mahler measure
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- by Valérie Flammang, Georges Rhin and Jean-Marc Sac-Épée;
- Math. Comp. 75 (2006), 1527-1540
- DOI: https://doi.org/10.1090/S0025-5718-06-01791-1
- Published electronically: March 28, 2006
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Abstract:
In this work, we show how suitable generalizations of the integer transfinite diameter of some compact sets in $\mathbb {C}$ give very good bounds for coefficients of polynomials with small Mahler measure. By this way, we give the list of all monic irreducible primitive polynomials of $\mathbb {Z}[X]$ of degree at most $36$ with Mahler measure less than $1. 324...$ and of degree $38$ and $40$ with Mahler measure less than $1. 31$.References
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Bibliographic Information
- Valérie Flammang
- Affiliation: UMR CNRS 7122, Département de Mathématiques, UFR MIM, Université de Metz, Ile du Saulcy, 57045 Metz Cedex 01, France
- MR Author ID: 360354
- Email: flammang@poncelet.univ-metz.fr
- Georges Rhin
- Affiliation: UMR CNRS 7122, Département de Mathématiques, UFR MIM, Université de Metz, Ile du Saulcy, 57045 Metz Cedex 01, France
- Email: rhin@poncelet.univ-metz.fr
- Jean-Marc Sac-Épée
- Affiliation: UMR CNRS 7122, Département de Mathématiques, UFR MIM, Université de Metz, Ile du Saulcy, 57045 Metz Cedex 01, France
- Email: jmse@poncelet.univ-metz.fr
- Received by editor(s): November 24, 2004
- Received by editor(s) in revised form: February 8, 2005
- Published electronically: March 28, 2006
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 75 (2006), 1527-1540
- MSC (2000): Primary 11Y40, 11R06
- DOI: https://doi.org/10.1090/S0025-5718-06-01791-1
- MathSciNet review: 2219043