{"schema":"vela.problem-packet.v0.1","problem":995,"statement":"Let $n_1<n_2<\\cdots$ be a lacunary sequence of integers and $f\\in L^2([0,1])$. Estimate the growth of, for almost all $\\alpha$,\\[\\sum_{1\\leq k\\leq N}f(\\{ \\alpha n_k\\}).\\]For example, is it true that, for almost all $\\alpha$,\\[\\sum_{1\\leq k\\leq N}f(\\{ \\alpha n_k\\})=o(N\\sqrt{\\log\\log N})?\\]","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)"}