Conditional estimates for error terms related to the distribution of zeros of ζ′(s)

Berndt, Levinson and Montgomery investigated the distribution of nonreal zeros of derivatives of the Riemann zeta function, including the number of zeros up to a height T and the distribution of the real part of nonreal zeros. In this paper we obtain sharper estimates for the error terms of their results in the case of the first derivative of the Riemann zeta function, under the truth of the Riemann hypothesis.