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Endpoint and Vanishing-Density Asymptotics for Hardy--Szegő Zero Counts
We study the number \(N_I(L)\) of zeros of the Hardy--Szegő zero process in the horizontal window \([0,L]\times I\) as \(L\to\infty\), where \(I=[α,β]\Subset(0,\infty)\) is fixed. We obtain sharp point-probability asymptotics at the lower endpoint of the density scale. In the fixed-count regime, for
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