On small distances between ordinates of zeros of $ζ(s)$ and $ζ'(s)$

Details On small distances between ordinates of zeros of $ζ(s)$ and $ζ'(s)$ On small distances between ordinates of zeros of $ζ(s)$ and $ζ'(s)$

2006-10-11

arxiv.org/abs/math/0610377v2

Mathematics

Number Theory

In the revised version, by using Theorem 1 and an idea of Haseo Ki, we obtain a substantial improvement upon the older version

Scientific paper

We prove that for any zero $\beta'+i\gamma'$ of $\zeta'(s)$ there exists a
zero $\beta+i\gamma$ of $\zeta(s)$ such that $|\gamma-\gamma'|\ll
\sqrt{|\beta'-\tfrac{1}{2}|},$ and we provide some other related results.

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