2 Department of Mathematics and Statistics, Queen’s University
3 Departement of Mathematics and Statistics [Kingston, Queen's University]
We consider the k-higher Mahler measure mk(P) of a Laurent polynomial P as the integral of logk|P| over the complex unit circle and zeta Mahler measure as the generating function of the sequence mk(P). In this paper we derive a few properties of the zeta Mahler measure of the polynomial Pn(z):=(zN−1)/(z−1) and propose a conjecture.