Zeros of derivatives of $L$-functions in the Selberg class on $\Re(s)<1/2$

Abstract

In this article, we show that the Riemann hypothesis for an L-function F belonging to the Selberg class implies that all the derivatives of F can have at most finitely many zeros on the left of the critical line with imaginary part greater than a certain constant. This was shown for the Riemann zeta function by Levinson and Montgomery in 1974.