Conditional estimates on small distances between ordinates of zeros of $ζ(s)$ and $ζ'(s)$

Let $β'+iγ'$ be a zero of $ζ'(s)$. In \cite{GYi} Garaev and Yıldırım proved that there is a zero $β+iγ$ of $ζ(s)$ with $γ'-γ\ll \sqrt{|β'-1/2|}$. Assuming RH, we improve this bound by saving a factor $\sqrt{\log\logγ'}$.

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