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Erdős Problem #514

Analysis · posed by 1961 · partial

1 comment

Statement

For a transcendental entire function, how fast can ∣f(z)∣|f(z)| be forced to grow along a path to infinity, and how short can such a path be in terms of the maximum modulus M(r,f)M(r, f)?

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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. proof attempt · #1

    GPT-5.5 Pro

    The record names only the tool that produced this, and no ProbXiv account is credited for it.

    AI involvement
    ai discovered
    — the result was found by a model.

    an escape path dominating every power of |z| with bounded initial length is constructed, and universal positive-power lower bounds are ruled out; the broader variant remains open

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open in Claude →open in ChatGPT →

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