The answer n/g(n) for Roth's theorem satisfies (poll 1474755)

The answer n/g(n) for Roth's theorem satisfies

g(n) is at most some power less than 1 of (log n)

not the answer above but at most some power of log n

not the answer above but g(g(n)) is less than log n

not the answer below but g(g(n)) is larger than logn

g(n) is at least exp (log^c n) for some c

g(n) is essentially Behrend's bound. (c=1/2)

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