{"schema":"vela.problem-packet.v0.1","problem":523,"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 $0\\leq k\\leq n$. Does there exist some constant $C>0$ such that, almost surely,\\[\\max_{\\lvert z\\rvert=1}\\left\\lvert \\sum_{k\\leq n}\\epsilon_k(t)z^k\\right\\rvert=(C+o(1))\\sqrt{n\\log n}?\\]","status":"solved","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)"}