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 prettier.

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?