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# Speiser's criterion

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A. Speiser (Math Annahlen 110 (1934) 514-521) proved that the Riemann Hypothesis
is equivalent to the non-vanishing of the derivative $\zeta'(s)$ in the left-half of the critical strip $0<\sigma< 1/2.$ Levinson and Montgomery [\begin{rawhtml}MR 54 \#5135\end{rawhtml}]
gave an alternative, quantitative version of this result which led to Levinson's
[\begin{rawhtml}MR 58 \#27837\end{rawhtml}] discovery of his method for counting zeros on the critical line. He then proceeded to prove that at least 1/3 of the zeros of $\zeta(s)$ are on the critical line.\begin{rawhtml}

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