New Methods Providing High Degree Polynomials with Small Mahler Measure

Abstract

In this work, we propose two new methods devoted to provide a large list of new polynomials with high degree and small Mahler measure. First, by statistical considerations, we augment Mossinghoff's list of polynomials with degree at most 180, and then we give a new list of such polynomials of degree up to 300. The second idea is to perturb polynomials of Mossinghoff's list, and for higher degrees, of this new list, and to use them as initial polynomials for a minimization method, which converges to new polynomials with lower Mahler measure.