maximum of modulus polynomial of degree $n$ in circle of radius 1

Asked Mar 26 '21 at 18:14

Active Mar 26 '21 at 18:14

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Good time of day. Can you help me please with this task? Consider a polynomial of degree $n$ with leading coefficient equal to 1. Prove that the maximum of its modulus in a circle of radius 1 not less than one. When it is equal to one?

I tried to use Rouche's theorem. But it was unsuccessful. Thank you

asked Mar 26 '21 at 18:14

UserIn

See as well here – Jean Marie Mar 26 '21 at 18:28
Another one: https://math.stackexchange.com/q/1749037/42969. – Martin R Mar 26 '21 at 18:42
In the given reference, the solution found by the asker using Cauchy integral formula is remarkably simple ! – Jean Marie Mar 26 '21 at 19:13

maximum of modulus polynomial of degree $n$ in circle of radius 1

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