# The generalised Shanks's conjecture

Speaker: Andrew Pearce-Crump

Date: Mon, Jul 25, 2022 to Tue, Jul 26, 2022

Conference: Moments of L-functions Workshop

Subject:

Class: Scientific

### Abstract:

Shanks's conjecture states that for $\rho$ a non-trivial zero of the Riemann zeta function $\zeta (s)$, we have that $\zeta ' (\rho)$ is real and positive in the mean. We show that this generalises to all order derivatives, with a natural pattern that comes from the leading order of the asymptotic result. We give an idea of the proof, and a discussion on the error term.