Zeros of the derivatives of the Riemann zeta-function

Abstract

Levinson and Montgomery in 1974 proved many interesting formulae on the zeros of derivatives of the Riemann zeta function $\zeta(s)$. When Conrey proved that at least 2/5 of the zeros of the Riemann zeta function are on the critical line, he proved the asymptotic formula for the mean square of $\zeta(s)$ multiplied by a mollifier of length $ T^{4/7}$ near the $1/2$-line. As a consequence of their papers, we study some aspects of zeros of the derivatives of the Riemann zeta function with no assumption.