Apparently the negation of RH is enough to state that there needs to be infinitely many numbers such that d(n)<=0. That would imply that you can find arbitraril

Apparently the negation of RH is enough to state that there needs to be infinitely many numbers such that d(n)<=0. That would imply that you can find arbitrarily large n such that d(n)<=0, but I don't think that's enough to claim that "lim sup (n->infinity) (d(n)) <= 0". I think it's enough to claim "lim inf (n->infinity) (d(n)) <= 0" though, but for some reason they proved that in a different way, that I don't quite understand yet.