Integer transfinite diameter and polynomials with small Mahler measure

Abstract

In this work, we show how suitable generalizations of the integer transfinite diameter of some compact sets in 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 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.