I'm working on a problem in multiplicative ergodic theory, and Mahler measure has just made *another* appearance. I am looking for a uniform lower bound on Mahler measure over all polynomials of *fixed degree* with complex coefficients where the largest coefficient is of absolute value 1. 

I found an ugly bound that is exponential in the degree, but am hoping for something in the literature or something a bit prettier. 

<blockquote>
Can anyone give me a reference (or simple argument) for a lower bound for Mahler measure of degree $d$ polynomials in a single variable (with complex coefficients) where the largest coefficient is of absolute value 1?
</blockquote>