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On the distribution of values of the derivative of the Riemann zeta function at its zeros. I
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Number theory, algebra, and analysis, Tome 276 (2012), pp. 57-82 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $\zeta'(s)$ be the derivative of the Riemann zeta function $\zeta(s)$. A study on the value distribution of $\zeta'(s)$ at the non-trivial zeros $\rho$ of $\zeta(s)$ is presented. In particular, for a fixed positive number $X$, an asymptotic formula and a non-trivial upper bound for the sum $\sum_{0\operatorname{Im}\rho\leq T}\zeta'(\rho)X^\rho$ as $T\to\infty$ are given. We clarify the dependence on the arithmetic nature of $X$. 
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     author = {Akio Fujii},
     title = {On the distribution of values of the derivative of the {Riemann} zeta function at its {zeros.~I}},
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Akio Fujii. On the distribution of values of the derivative of the Riemann zeta function at its zeros. I. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Number theory, algebra, and analysis, Tome 276 (2012), pp. 57-82. http://geodesic.mathdoc.fr/item/TM_2012_276_a5/

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