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erdos_40

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For what functions $g(N) → \infty$ is it true that $$\lvert A\cap \{1,\ldots,N\}\rvert \gg \frac{N^{1/2}}{g(N)}$$ implies $\limsup 1_A\ast 1_A(n)=\infty$?

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Lean 4 Statement 
theorem erdos_40 : Erdos40ForSet answer(sorry)
ID: ErdosProblems__40__erdos_40
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