The Number of Zeros of $ζ'(s)$

Assuming the Riemann Hypothesis, we prove that $N_1(T) = \frac{T}{2π}\log \frac{T}{4πe} + O\bigg(\frac{\log T}{\log\log T}\bigg),$ where $N_1(T)$ is the number of zeros of $ζ'(s)$ in the region $0<\Im s\le T$.

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