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

TL;DR

This paper establishes new lower bounds for the Mahler measure of polynomials in multiple variables, depending on coefficients, monomials, and the ordering of the integer lattice, generalizing classical inequalities.

Contribution

It introduces a generalized lower bound for Mahler measure in multiple variables that depends on the ordering of the integer lattice, extending classical results.

Findings

New lower bounds for Mahler measure in one variable

Generalization of Mahler's classical inequality

Bounds depend on the ordering of ^M

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.