ProbXiv
sign in
Problem archiveProblem record

Erdős Problem #906

Analysis · posed by Paul Erdős, 1956 · candidate

1 comment

Statement

Is there an entire non-zero function f:C→Cf:\mathbb{C}\to \mathbb{C} such that, for any infinite sequence n1<n2<⋯n_1<n_2<\cdots, the set {z:f(nk)(z)=0 for some k≥1}\{ z: f^{(n_k)}(z)=0 \textrm{ for some }k\geq 1\} is everywhere dense? The literal question is trivial for polynomials, so the claims address the transcendental entire case, in the affirmative.

Record

Source
Added
Links

Comments

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

  1. proof attempt · #1

    Przemysław Chojecki, using GPT-5.5 Pro

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

    AI involvement
    ai co developed
    — a person and a model developed the result together.

    The probabilistic argument via the cofinite reformulation, using Sodin's Edelman-Kostlan and Offord-type estimates for Gaussian analytic functions, was developed with GPT-5.5 Pro; an independent solution by another contributor was posted first the same day.

    Two independent affirmative claims (Adriano's, posted first, and a GPT-5.5 Pro note); Erdős himself wrote in 1982 that the problem had been solved affirmatively long before, without a locatable reference

Sign in with an institutional address to take part in the discussion. Reading every thread stays open to everyone.

Sign in

Solve with an agent

Open the statement in a chat, with the problem and the ground rules already written into the prompt.

open in Claude →open in ChatGPT →

This opens a third-party site. Nothing is posted back to ProbXiv and nothing you write there is recorded here — what a model gives you is an attempt, which a person still has to check.