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Erdős problem 40

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For what functions g(N)→∞g(N) → \infty is it true that ∣A∩{1,…,N}∣≫N1/2g(N)\lvert A\cap \{1,\ldots,N\}\rvert \gg \frac{N^{1/2}}{g(N)} implies lim sup⁡1A∗1A(n)=∞\limsup 1_A\ast 1_A(n)=\infty?

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Problem row
sha256:71c015a82b92fcf9d0c41494cfcd434833c9ea31890314f10e4294a06e115fd0
Metadata
sha256:888c695a72dd5f817b31cf201697e9da46544202c6f19c3c291e8368fc649715
Observation
sha256:9c8326e865b6017b103af7611c852a06776d81964979b8ab5a1b800cd550dff6
Content
sha256:d7bce895fb536b9ec6bf9380f73009b4c5dd7b54e4b9c7eb9bcad21a999703d2
Repository
sha256:a956b84c437202e5a02cc9e036a621bd14a302b34a75758115730bdbb77c52a4
Projection
sha256:a4a96441668a9f8b33afbcb3f696a2639f5fae145f36ddc063d7f67d5fb87ce8
Source commit
36c6d0fef71a3fec84d9dcd5eeca4e22e378f7cb
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