Let $f = \sum_{n = 0}^{\infty} a_{n} z^{n}$ be a transcendental entire function. What is the greatest possible value of $r \to \infty lim inf \frac{max _{n} ∣ a _{n} r ^{n} ∣}{max _{∣ z ∣ = r} ∣ f ( z )∣} ?$

Worked, still open.

analysis · open · formalized (Lean) · 0 attempts

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vela registry pull vfr_37aec80d874a0239

vela reproduce examples/erdos-problems

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unverified AI candidates (2)

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

This is **not known exactly**: it’s an open problem of Erdős (Erdős Problem **#513**). ([Erdős Problems][1])

llm-hunter · gpt pro 5.2 · unverified

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

AMS 30 · open (literature)

theorem erdos_513 : answer(sorry) =
    ⨆ f : {f : ℂ → ℂ // Transcendental ℂ[X] f ∧ Differentiable ℂ f},
    (liminf (fun r : ℝ => ratio r f) atTop)

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