On Univalent Polynomials

Abstract

We define Vn Q C_1 to be the set of (n -l)-tuples {a2,.■ ■ ,an) such that the polynomial />(z) -z + a2z2 + • ■ ■ + anz" is univalent, i.e., one-to-one in \z\ < 1.In this paper we construct a real polynomial h of degree 4(2(n -1) -l)(n -1) such that if (a2,...,an) is in the boundary of Vn then h(Re a2, Im a2,..., Re an, Im an ) = 0.This shows that the boundary of Vn is a subset of an algebraic submanifold of Ä2'"-1'.

Locations

• Proceedings of the American Mathematical Society - View - PDF