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The number of zeros and the distribution of the real part of non-real zerosof the derivatives of the Riemann zeta function have been investigated byBerndt, Levinson, Montgomery, and Akatsuka. Berndt, Levinson, and Montgomeryinvestigated the general case, meanwhile Akatsuka gave sharper estimates forthe first derivative of the Riemann zeta function under the truth of theRiemann hypothesis. In this paper, we extend the results of Akatsuka to thesecond derivative of the Riemann zeta function.

On the zeros of the second derivative of the Riemann zeta function under the Riemann hypothesis