Control theory and the Riemann hypothesis: A roadmap

TL;DR

This paper explores a novel approach to the Riemann hypothesis using control theory, constructing a transfer function from the zeta function and linking the hypothesis to the convergence of a series expansion of the impulse response.

Contribution

It introduces a control theoretic framework for the Riemann hypothesis, connecting the hypothesis to the convergence properties of a series derived from the zeta function.

Findings

Proposes a transfer function based on the zeta function

Develops a series expansion for the impulse response

Links the truth of the Riemann hypothesis to the convergence of this series

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.