Control theory and the Riemann hypothesis: A roadmap

Abstract

An alternative way of looking at the Riemann hypothesis from the viewpoint of mathematical control theory is considered. A control theoretic transfer function is constructed by inverting the values of the Riemann zeta-function from which the unstable pole at s=1 has been stripped off. A series expansion is developed for the impulse response of the control system via inverse Laplace transformation. If the series converges and the unproved growth conjecture of the impulse response is true, then the Riemann hypothesis is also true.