{"schema":"vela.problem-packet.v0.1","problem":40,"statement":"For what functions $g(N)\\to \\infty$ is it true that\\[\\lvert A\\cap \\{1,\\ldots,N\\}\\rvert \\gg \\frac{N^{1/2}}{g(N)}\\]implies $\\limsup 1_A\\ast 1_A(n)=\\infty$?","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)"}