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March 1973 Zeros of $\zeta^{\prime} (s)$ and the Riemann hypothesis
Robert Spira
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Illinois J. Math. 17(1): 147-152 (March 1973). DOI: 10.1215/ijm/1256052045


It is shown that the Riemann hypothesis implies that the derivative of the Riemann zeta function has no zeros in the open left half of the critical strip. It is also shown, with no hypothesis, that, with the exception of a bounded region where the zeros can be calculated, the closed left half plane contains only real zeros of the derivative. It is further shown that the Riemann hypothesis is equivalent to the condition that $|\zeta(s)|$ increases as $\mathrm{Re}\,s$ moves left from $1/2$ for $\mathrm{Im}\,s$ sufficiently large.


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Robert Spira. "Zeros of $\zeta^{\prime} (s)$ and the Riemann hypothesis." Illinois J. Math. 17 (1) 147 - 152, March 1973.


Published: March 1973
First available in Project Euclid: 20 October 2009

zbMATH: 0247.10022
MathSciNet: MR0309881
Digital Object Identifier: 10.1215/ijm/1256052045

Primary: 10H05

Rights: Copyright © 1973 University of Illinois at Urbana-Champaign

Vol.17 • No. 1 • March 1973
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