This article is cited in 10 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 $X$.

UDC: 511.331

Received in August 2011

Language: English

 English version: Proceedings of the Steklov Institute of Mathematics, 2012, 276, 51–76

Bibliographic databases:

• 
• 
• 
•