An adelic causality problem related to abelian L-functions

Abstract

I associate to a global field K a Lax-Phillips scattering which has the property of causality if and only if the Riemann Hypothesis holds for all the abelian L-functions of K. As a Hilbert space closure problem this provides an adelic variation on a theme initiated by Nyman and Beurling. The adelic aspects are related to previous work by Tate, Iwasawa and Connes.