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If $p(z)\in\mathbb{C}[z]$ is a monic polynomial of degree $n$ then is the length of the curve $\{ z\in \mathbb{C} : \lvert p(z)\rvert=1\}$ maximised when $p(z)=z^n-1$?
#114
:
[Er61,p.247]
[Er90]
polynomials
,
analysis
Additional thanks to
: Geoffrey Irving
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