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Integer transfinite diameter and polynomials with small Mahler measure

Authors:	Valé rie Flammang Georges Rhin Jean-Marc Sac-É pé e

Institution:	UMR CNRS 7122, Département de Mathématiques, UFR MIM, Université de Metz, Ile du Saulcy, 57045 Metz Cedex 01, France ; UMR CNRS 7122, Département de Mathématiques, UFR MIM, Université de Metz, Ile du Saulcy, 57045 Metz Cedex 01, France ; UMR CNRS 7122, Département de Mathématiques, UFR MIM, Université de Metz, Ile du Saulcy, 57045 Metz Cedex 01, France

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 with Mahler measure less than $1.\,324...$ and of degree and with Mahler measure less than $1.\,31$ .

Keywords:	Mahler measure integer transfinite diameter explicit auxiliary function

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