Zeros of \zeta^{''}(s) & \zeta^{'''}(s) in \sigma< 1/2

Authors: CEM YALÇIN YILDIRIM

Abstract: There is only one pair of non-real zeros of $\zeta^{''}(s)$, and of $\zeta^{'''}(s)$, in the left half-plane. The Riemann Hypothesis implies that $\zeta''(s)$ and $\zeta'''(s)$ have no zeros in the strip $0 \leq \Re\,s < {1\over 2} $.

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