Illinois Journal of Mathematics

Zeros of $\zeta^{\prime} (s)$ and the Riemann hypothesis

Robert Spira

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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.

Article information

Illinois J. Math. Volume 17, Issue 1 (1973), 147-152.

First available in Project Euclid: 20 October 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 10H05


Spira, Robert. Zeros of $\zeta^{\prime} (s)$ and the Riemann hypothesis. Illinois J. Math. 17 (1973), no. 1, 147--152.

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