Integer transfinite diameter and polynomials with small Mahler measure

Flammang, Valérie; Rhin, Georges; Sac-Épée, Jean-Marc

doi:10.1090/S0025-5718-06-01791-1

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 $1. 31$.

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