Abstract :
We associate to the 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.
