On the Absolute Trace of Polynomials Having All Zeros in a Sector

Abstract

Let α be an algebraic integer all of whose conjugates lie in a sector |arg z| ≤ θ with 0 ≤ θ < 90°. Using the method of explicit auxiliary functions, we compute the greatest lower bound υ(θ) of the absolute trace of α, for θ belonging to seven subintervals of [0, 90°). The polynomials involved in the auxiliary functions are found by Wu's algorithm.

Keywords:

• Primary 11R04, 11Y40, 12D10
• Algebraic integer
• trace
• explicit auxiliary functions
• integer transfinite diameter