Grace–Walsh–Szegő coincidence theorem

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

Suppose ƒ(z₁, ..., z_n) 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 ${\displaystyle \zeta _{1},\ldots ,\zeta _{n}\in A}$ there exists ${\displaystyle \zeta \in A}$ such that

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