MathDB

Let

q{}

be an arbitrary polynomial with complex coefficients which is not identically

0

and

\Gamma_q =\{z : |q(z)| = 1\}

be its contour line. Prove that for every point

z_0\in\Gamma_q

there is a polynomial

p{}

for which

|p(z_0)| = 1

and

|p(z)|<1

for any

z\in\Gamma_q\setminus\{z_0\}.

Problem Statement