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

Fan Ge

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arXiv · 1604.04243

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

Fan Ge

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Abstract

Let $\beta'+i\gamma'$ be a zero of $\zeta'(s)$. In \cite{GYi} Garaev and Y{\i}ld{\i}r{\i}m proved that there is a zero $\beta+i\gamma$ of $\zeta(s)$ with $ \gamma'-\gamma \ll \sqrt{|\beta'-1/2|} $. Assuming RH, we improve this bound by saving a factor $\sqrt{\log\log\gamma'}$.

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Fan Ge. 2016-04-14. Conditional estimates on small distances between ordinates of zeros of $\zeta(s)$ and $\zeta'(s)$. https://arxiv.org/abs/1604.04243

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