Grace–Walsh–Szegő theorem


In mathematics, the Grace–Walsh–Szegő coincidence theorem is a result named after John Hilton Grace, Joseph L. Walsh, and Gábor Szegő.

Statement

Suppose ƒ is a polynomial with complex coefficients, and that it is
Let A be a circular region in the complex plane. If either A is convex or the degree of ƒ is n, then for every there exists such that