An adelic causality problem related to abelian L-functions
Abstract
Description
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.
18 pages, latex2e with amsfonts. Final version, accepted for publication
18 pages, latex2e with amsfonts. Final version, accepted for publication