OPENNOTORIOUSnumber theoryadditive basis
For what functions $g(N)\to \infty$ is it true that $|A\cap \{1,\ldots,N\}| \gg N^{1/2}/g(N)$ implies $\limsup 1_A\ast 1_A(n)=\infty$?
Notes: This is a stronger formulation of the Erdos-Turan conjecture (problem 28). Solving it for any g(N) -> infinity would resolve problem 28.
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