A new reason for doubting the Riemann hypothesis

Abstract

We make plausible the existence of counterexamples to the Riemann hypothesis located in the neighbourhood of unusually large peaks of $|\zeta |$. The main ingredient in our argument is an identity which links the zeros of a function $f$ defined on the interval $[-a,a]$ and the values of its derivatives of odd order at $\pm a$.

17 pages, 1 figure