An adelic causality problem related to abelian L-functions
Number Theory
2007-05-23 v3
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.
Cite
@article{arxiv.math/0001013,
title = {An adelic causality problem related to abelian L-functions},
author = {Jean-Francois Burnol},
journal= {arXiv preprint arXiv:math/0001013},
year = {2007}
}
Comments
18 pages, latex2e with amsfonts. Final version, accepted for publication