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 $M$ variables our result depends on ${\mathbb{Z}}^M$ as an ordered group, and in general our lower bound depends on the choice of ordering.

References in corpus (1)

• A generalization of a theorem of Boyd and Lawton

Cited by in corpus (1)

• Limits of Mahler measures in multiple variables