= Asymptotic inversion of the zeta zero count
{title2=$\gamma_n\sim2\pi n/\log n$}
List positive ordinates of <Nontrivial zeros of the Riemann zeta function> in nondecreasing order, including multiplicity. The <Riemann–von Mangoldt formula> gives $N(T)\sim T\log T/(2\pi)$. For each fixed $\varepsilon>0$, evaluate this at $T=(1\pm\varepsilon)2\pi n/\log n$ to bracket the $n$th ordinate. Letting $\varepsilon$ decrease to zero proves the displayed asymptotic without assuming simple zeros or distinct ordinates.
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