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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/125841We prove that for any zero $β'+iγ'$ of $ζ'(s)$ there exists a zero $β+iγ$ of $ζ(s)$ such that $|γ-γ'|\ll \sqrt{|β'-\tfrac{1}{2}|},$ and we provide some other related results.In the revised version, by using Theorem 1 and an idea of Haseo Ki, we obtain a substantial improvement upon the older version of Theorem 3Number Theory11M26; 11M06On small distances between ordinates of zeros of $ζ(s)$ and $ζ'(s)$text