Asymptotic Location of the Zeros of the Faber Polynomials

Let E be a compact set of the complex plane containing more than one point whose complement in the extended complex plane is simply connected. Let ω = φ(z) map conformally Ext(E) into ω>1 and with φ(∞)=∞. The map φ(z) has the form φ(z)=z/c+a₀+a₋₁ z +a₋₂z²+ ⋯ The Faber polynomials for E, φₙ(z), consist of the polynomial part of φ(z)ⁿ. For ε>0 given let E_ε:=zB(z,ε), where B(z,ε) denotes the disk of center z and radius ε, and let B_ε:=Br(E_ε). Letα:=infz(E)~\θ;~πθis the exterior angle ofEat z\. A typical result obtained in this work is the Theorem 3.2. 2000 Mathematics Subject Classification. 31E10, 41A10, 41A29, 41A40