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- Jan 26, 2012

- 995

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**Problem**: Let $p(z)$ be a polynomial of degree $n$ that is nonzero on the unit circle $\mathbb{T}=\{z:|z|=1\}$. Define $m_0$ by the formula

\[m_0=\frac{1}{2\pi i}\int_{\mathbb{T}}\frac{p^{\prime}(z)}{p(z)}\,dz.\]

Show that $m_0\in\{0,\ldots,n\}$.

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