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Erdős problem 990

Let f=a0+⋯+adxd∈C[x]f=a_0+\cdots+a_dx^d\in \mathbb{C}[x] be a polynomial. Is it true that, if ff has roots z1,…,zdz_1,\ldots,z_d with corresponding arguments θ1,…,θd∈[0,2π]\theta_1,\ldots,\theta_d\in [0,2\pi], then for all intervals I⊆[0,2π]I\subseteq [0,2\pi] ∣(#θi∈I)−∣I∣2πd∣≪(nlog⁡M)1/2, \left\lvert (\# \theta_i \in I) - \frac{\lvert I\rvert}{2\pi}d\right\rvert \ll \left(n\log M\right)^{1/2}, where nn is the number of non-zero coefficients of ff and M=∣a0∣+⋯+∣ad∣(∣a0∣∣ad∣)1/2. M=\frac{\lvert a_0\rvert+\cdots +\lvert a_d\rvert}{(\lvert a_0\rvert\lvert a_d\rvert)^{1/2}}.

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Reported by these sources. Not reviewed here.

  • Formalization

    Erdős AI contributions wiki · 10 Apr, 2026

    Machine
    GPT-5.4 Pro
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  • AI standalone

    Erdős AI contributions wiki · 9 Apr, 2026

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    OpenAI internal model
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  • construction

    VibeMathed

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    OpenAI internal model
    People
    Boris Alexeev, Moe Putterman, Mehtaab Sawhney, Mark Sellke, Gregory Valiant
    Reported outcome
    resolved
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