On the absolute mahler measure of polynomials having all zeros in a sector. II

Let alpha be an algebraic integer of degree d, not 0 or a root of unity, all of whose conjugates alpha(i) are confined to a sector \arg z\ less than or equal to theta. In the paper On the absolute Mahler measure of polynomials having all zeros in a sector, G. Rhin and C. Smyth compute the greatest lower bound c(theta) of the absolute Mahler measure (Pi(i=1)(d) max(1,\alpha(i)\))(1/d) of alpha, for theta belonging to nine subintervals of [0, 2pi/3]. In this paper, we improve the result to thirteen subintervals of [0, pi] and extend some existing subintervals.