Scattering for time series with an application to the zeta function of an algebraic curve

Abstract

I explain how the Lax-Phillips theory can be applied to a purely innovating time series and compute the corresponding scattering function. I then associate such a time series to an algebraic curve (of genus at least 1) over a finite field and show that the Riemann Hypothesis (proven long ago) holds if and only if the scattering is causal (this causality is not independently established, though).