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arXiv · 1510.04359

The distribution of zeros of $ζ'(s)$ and gaps between zeros of $ζ(s)$

Fan Ge
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Abstract

Assume the Riemann Hypothesis, and let $γ^+>γ>0$ be ordinates of two consecutive zeros of $ζ(s)$. It is shown that if $γ^+-γ< v/ \log γ$ with $v<c$ for some absolute positive constant $c$, then the box $$ \{s=σ+it: 1/2<σ<1/2+v^2/4\logγ, γ\le t\le γ^+\} $$ contains exactly one zero of $ζ'(s)$. In particular, this allows us to prove half of a conjecture of Radziwiłł in a stronger form. Some related results on zeros of $ζ(s)$ and $ζ'(s)$ are also obtained.

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Fan Ge. 2015-10-15. The distribution of zeros of $ζ'(s)$ and gaps between zeros of $ζ(s)$. https://arxiv.org/abs/1510.04359

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