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

Abstract

In this article, we show that the Riemann hypothesis for an L L -function F F belonging to the Selberg class implies that all the derivatives of F 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 [Acta Math. 133 (1974), pp. 49–65].