{"schema":"vela.problem-packet.v0.1","problem":987,"statement":"Let $x_1,x_2,\\ldots \\in (0,1)$ be an infinite sequence and let\\[A_k=\\limsup_{n\\to \\infty}\\left\\lvert \\sum_{j\\leq n} e(kx_j)\\right\\rvert,\\]where $e(x)=e^{2\\pi ix}$.Is it true that\\[\\limsup_{k\\to \\infty} A_k=\\infty?\\]Is it possible for $A_k=o(k)$?","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)"}