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Erdős Problem #522

Probability & statistics · posed by 1961 · candidate

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Statement

For Pn(z)=∑k=0nεkzkP_n(z) = \sum_{k=0}^n \varepsilon_k z^k with independent uniform signs, does the number RnR_n of roots in ∣z∣≤1|z| \le 1 satisfy Rn/(n/2)→1R_n/(n/2) \to 1 almost surely? The manuscript proves the strong law with Rn=n/2+Oω(n149/150)R_n = n/2 + O_\omega(n^{149/150}).

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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

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    VibeMathed records no account of how GPT-5.5 Pro was used here. See erdosproblems.com/522.

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