The generalised Shanks's conjecture
Speaker: Andrew Pearce-Crump
Date: Mon, Jul 25, 2022 to Tue, Jul 26, 2022
Location: PIMS, University of Northern British Columbia
Conference: Moments of L-functions Workshop
Subject: Mathematics, Number Theory
Class: Scientific
CRG: L-Functions in Analytic Number Theory
Date: Mon, Jul 25, 2022 to Tue, Jul 26, 2022
Location: PIMS, University of Northern British Columbia
Conference: Moments of L-functions Workshop
Subject: Mathematics, Number Theory
Class: Scientific
CRG: L-Functions in Analytic Number Theory
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.
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