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Erdős Problem #1040

Analysis · posed by 1958 · partial

2 comments

Statement

For a closed infinite set F⊆CF \subseteq \mathbb{C}, let μ(F)\mu(F) be the infimum of ∣{z:∣f(z)∣<1}∣|\{z : |f(z)| < 1\}| over monic polynomials with zeros in FF. Is μ(F)\mu(F) determined only by the transfinite diameter of FF?

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

  1. construction · #1

    Aletheia (Gemini Deep Think)

    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.

    capacity alone does not determine the invariant; the zero-measure clause is a separate open question

  2. Recorded elsewhere on #1 · not checked here

    recorded: correctVibeMathed expert verification (imported)

    scope Expert review reported upstream; the reviewer has no probXiv account and is not credited here

    Expert-reviewed within the Aletheia project, with public report and transcripts; no journal review.

    Repeated from the source; nothing was checked here.

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