On the absolute Mahler measure of polynomials having all zeros in a sector. III
Valérie Flammang, Georges Rhin · Mathematics of Computation · 2015
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 lie in a sector | arg z | ≤ θ \vert \arg z \vert \leq \theta . In 1995, G. Rhin and C. Smyth computed 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, | \alpha _i |))^{1/d} of α \alpha , for θ \theta belonging to nine subintervals of [ 0 , 2 π / 3 ] [0, 2 \pi /3] . More recently, in 2004, G. Rhin and Q. Wu improved the result to thirteen subintervals of [