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.

arXiv comment16 pages with large spacings, comments welcome

References in corpus (1)

• Zeros of the first derivative of Dirichlet $L$-functions