If p(z)∈C[z] is a monic polynomial of degree n then is the length of the curve z∈ C : | p(z)|=1 maximised when p(z)=z^n-1?

Erdős Problem #114 — 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 $p(z)=z^n-1$ ?

About 68 years old · traced to 1958

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 $p(z)=z^n-1$ ?

References

Primary source

ULAM AI, UnsolvedMath dataset, Erdős Problems set, revision b9437975f3c873f635a13c48f8b022f5ba80898a; CC BY 4.0.

Additional references

UnsolvedMath, Erdős Problems set, ULAM AI, licensed CC BY 4.0.

analysis polynomials

InErdős Problems

Posted 1 month ago · edited 3 weeks ago

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