Let $f (z)$ be an entire transcendental function. Does there exist a path $L$ so that, for every $n$ , $∣ f (z) / z^{n} ∣ \to \infty$ as $z \to \infty$ along $L$ ?Can the length of this path be estimated in terms of $M (r) = max_{∣ z ∣ = r} ∣ f (z)∣$ ? Does there exist a path along which $∣ f (z)∣$ tends to $\infty$ faster than a fixed function of $M (r)$ (such that $M (r)^{ϵ}$ )?

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unverified AI candidates (2)

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

* If $f$ is a **polynomial**, the answer is **no**: if (\deg f=d), then (\bigl|f(z)/z^n\bigr|\to 0) along every path for every (n>d).

llm-hunter · gpt pro 5.2 · unverified

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

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