- Thread starter
- Moderator
- #1
- Jan 26, 2012
- 995
Here's this week's problem.
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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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Remember to read the POTW submission guidelines to find out how to submit your answers!
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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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Remember to read the POTW submission guidelines to find out how to submit your answers!