Let $({ϵ}_k{)}_{k\ge 0}$ be independently uniformly chosen at random from $\{-1,1\}$. If $R_n$ counts the number of real roots of $f_n(z)={\sum }_{0\le k\le n}{ϵ}_k{z}^k$ then is it true that, almost surely,$$\underset{n\to \infty }{\lim }\frac{R_n}{\log n}=\frac{2}{\pi }?$$

gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

What *is* known for your Rademacher/Littlewood polynomials (f_n(x)=\sum_{k=0}^n \varepsilon_k x^k) is:

llm-hunter · gpt pro 5.2 · unverified

1 LLM attack(s) recorded (gpt pro 5.2); unverified.