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Proceedings of the American Mathematical Society

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Zeros of $ \zeta \sp{'} (s)$ in the critical strip


Author: Robert Spira
Journal: Proc. Amer. Math. Soc. 35 (1972), 59-60
MSC: Primary 10H05
DOI: https://doi.org/10.1090/S0002-9939-1972-0296035-5
MathSciNet review: 0296035
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Abstract: It is shown that the abscissa of convergence for the Dirichlet series $ {( - 1)^k}{(1 - {2^{1 - s}})^{k + 1}}{\zeta ^{(k)}}(s)$ is zero, where $ \zeta (s)$ is the Riemann zeta function. This implies the existence of infinitely many zeros of $ \zeta '(s)$ in the critical strip.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0296035-5
Keywords: Riemann zeta function
Article copyright: © Copyright 1972 American Mathematical Society

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