Mahler measure

Summary

The Mahler measure of a complex polynomial is the absolute value of its leading coefficient times a product over its roots. Each root outside the unit circle contributes its absolute value, and the other roots contribute $1$. It is multiplicative and, for integer polynomials, it is at least $1$. It measures the size of a polynomial in a way adapted to its roots. Small Mahler measures of integer polynomials are the subject of Lehmer's conjecture.