Seminar

The Mahler measure M(f) of a monic polynomial f is defined to be the absolute value of the product of those roots of f which lie outside the unit disk. The logarithmic Mahler measure m(f) = log M(f) turns out to be the integral of log|f| on the unit circle. In 1933, Lehmer essentially asked the following question: for any C >0, can we find a polynomial with integer coefficients such that 01,$ we define the k- higher Mahler measure to be the integral of log^k |f| on the unit circle. We explore the analogues of Lehmer's question for these higher Mahler measures. This is joint work with Matilde Lalin.