On the absolute Mahler measure of polynomials having all zeros in a sector. II
Georges Rhin, Qiang Wu · Mathematics of Computation · 2004
Let α \alpha be an algebraic integer of degree d d , not 0 0 or a root of unity, all of whose conjugates α i \alpha _{i} are confined to a sector | arg z | ≤ θ \vert \operatorname {arg} z \vert \le \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 ( θ ) c(\theta ) of the absolute Mahler measure ( ∏ i = 1 d max ( 1 , | α i | ) ) 1 / d \prod _{i=1}^{d} \max (1, \vert \alpha _{i} \vert ))^{1/d} of α \alpha , for θ \theta belonging to nine subintervals of [ 0 , 2 π / 3 ] [0, 2\pi /3] . In this paper, we improve the result to thirteen subintervals of