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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2012, Volume 276, Pages 57–82
(Mi tm3357)
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This article is cited in 7 scientific papers (total in 7 papers)
On the distribution of values of the derivative of the Riemann zeta function at its zeros. I
Akio Fujii Department of Mathematics, Rikkyo University, Tokyo, Japan
Abstract:
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 $X$.
Received in August 2011
Citation:
Akio Fujii, “On the distribution of values of the derivative of the Riemann zeta function at its zeros. I”, Number theory, algebra, and analysis, Collected papers. Dedicated to Professor Anatolii Alekseevich Karatsuba on the occasion of his 75th birthday, Trudy Mat. Inst. Steklova, 276, MAIK Nauka/Interperiodica, Moscow, 2012, 57–82; Proc. Steklov Inst. Math., 276 (2012), 51–76
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https://www.mathnet.ru/eng/tm3357 https://www.mathnet.ru/eng/tm/v276/p57
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Abstract page: | 406 | Full-text PDF : | 108 | References: | 50 |
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