“…for a certain cubic polynomial F 3 . In that regime, Lester and Yesha [30] showed that ∆ 2 (x, H), normalized to have unit mean-square using (1.6), has a Gaussian value distribution, at least for a narrow range of H below X 1/2 , the conjecture being that this should hold for X ǫ < H < X 1/2−ǫ for any ǫ > 0. For k ≥ 3, Milinovich and Turnage-Butterbaugh [31, p. 182] give an upper bound, assuming RH, of In concurrent work, Lester [29] shows that for k ≥ 3, assuming the Lindelöf Hypothesis, if h(x) = ( x X ) 1− 1 k X δ , (1.8)…”