Lower bounds for Mahler measure that depend on the number of monomials

Abstract

We prove a new lower bound for the Mahler measure of a polynomial in one and in several variables that depends on the complex coefficients and the number of monomials. In one variable, our result generalizes a classical inequality of Mahler. In [Formula: see text] variables, our result depends on [Formula: see text] as an ordered group, and in general, our lower bound depends on the choice of ordering.