{"schema":"vela.problem-packet.v0.1","problem":522,"statement":"Let $f(z)=\\sum_{0\\leq k\\leq n} \\epsilon_k z^k$ be a random polynomial, where $\\epsilon_k\\in \\{-1,1\\}$ independently uniformly at random for $0\\leq k\\leq n$. Is it true that, if $R_n$ is the number of roots of $f(z)$ in $\\{ z\\in \\mathbb{C} : \\lvert z\\rvert \\leq 1\\}$, then\\[\\frac{R_n}{n/2}\\to 1\\]almost surely?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}