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<h1 align=center> 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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Back to the 
<a href="http://www.aimath.org/WWN/rh/"> main index</a> 
for The Riemann Hypothesis.
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