For each fixed g, η_g(n)/√n converges to a positive finite limit, and α_g(n) = (1 + o_g(1))√(gn).
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Cardinalities of $g$-difference sets
For each fixed g, η_g(n)/√n converges to a positive finite limit, and α_g(n) = (1 + o_g(1))√(gn).