Mahler Measure and the ABC Inequality
by
Jeffrey D. Vaaler
University of Texas

We will describe an upper bound for the Mahler measure of the Wronskian of a collection of N+1 linearly independent polynomials with complex coefficients. If the coefficients of the polynomials are algebraic numbers a similar inequality holds at non-archimedean completions. Together these lead to an inequality for the absolute Weil heights of the roots of the polynomials. This later inequality is analogous to Mason's ABC inequality for polynomials. We will also discuss some applications to Diophantine problems.

Date received: May 14, 2004