Let $f(z)={\prod }_{i=1}^n(z-z_i)\in \mathbb{C}[x]$ where $|z_i|\le 1$ for all $i$. If $\Lambda (f)$ is the maximum of the lengths of the boundaries of the connected components of$$\{z:|f(z)|<1\}$$then determine the infimum of $\Lambda (f)$.

gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

Let [ f(z)=\prod_{i=1}^n (z-z_i),\qquad |z_i|\le 1, ] and let (\Lambda(f)) be the maximum [[nomath]](over connected components $U$ of ${|f|<1}$)[[/nomath]] of the boundary length (\mathrm{length}(\partial U)). The infimum is taken over **all such polynomials of all degrees (n\ge1)** (this is the “original” interpretati…

llm-hunter · gpt pro 5.2 · unverified

1 LLM attack(s) recorded (gpt pro 5.2); unverified.