An adelic causality problem related to abelian L-functions
arXiv:math/0001013 · doi:10.1006/jnth.2000.2616
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.
18 pages, latex2e with amsfonts. Final version, accepted for publication