Article
Distribution of the Values of the Derivative of the Riemann Zeta Function on Its a-Points
Authors
and
Abstract
In this paper, we study the value distribution of the derivative
\(\zeta'(s)\) of the Riemann zeta function at the \(a\)-points
\(\rho_a = \beta_a + i\gamma_a\) of \(\zeta(s)\). Actually, we give an
asymptotic formula and an upper bound for the sum
\[
\sum_{\rho_a;\ 0 < \gamma_a \le T} \zeta'(\rho_a)\, X^{\rho_a}
\quad \text{as } T \to \infty,
\]
where \(X\) is a fixed positive number. This work continues the
investigations of Fujii [1, 2, 3] and Garunkštis & Steuding [5].
Keywords
Riemann zeta function, a-points, value-distribution.
Citation
Jakhlouti, M. T. & Mazhouda, K. (2014). Distribution of the values of the derivative of the riemann zeta function on its a-points. Uniform Distribution Theory, 9(1), 115–125.
M. T. Jakhlouti and K. Mazhouda, “Distribution of the values of the derivative of the riemann zeta function on its a-points,” Uniform Distribution Theory, vol. 9, no. 1, pp. 115–125, 2014.
Jakhlouti MT, Mazhouda K. Distribution of the values of the derivative of the riemann zeta function on its a-points. Uniform Distribution Theory. 2014;9(1):115–125.
Jakhlouti, M. T. and Mazhouda, K. (2014), ‘Distribution of the values of the derivative of the riemann zeta function on its a-points’, Uniform Distribution Theory, 9(1), pp. 115–125.
Jakhlouti, Mohamed Taıb, and Kamel Mazhouda. “Distribution of the Values of the Derivative of the Riemann Zeta Function on Its A-points.” Uniform Distribution Theory, vol. 9, no. 1, 2014, pp. 115–125.
Jakhlouti, Mohamed Taıb, and Kamel Mazhouda. “Distribution of the Values of the Derivative of the Riemann Zeta Function on Its A-points.” Uniform Distribution Theory 9, no. 1 (2014): 115–125.
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Published by: Engineering Journals
