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arXiv · 2202.12126

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

Sneha Chaubey·Suraj Singh Khurana·Ade Irma Suriajaya
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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.

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Sneha Chaubey, Suraj Singh Khurana, Ade Irma Suriajaya. 2022-02-24. Zeros of derivatives of $L$-functions in the Selberg class on $\Re(s)<1/2$. https://doi.org/10.1090/proc/16251

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