An adelic causality problem related to abelian L-functions

Details An adelic causality problem related to abelian L-functions An adelic causality problem related to abelian L-functions

2000-01-04

arxiv.org/abs/math/0001013v3

J. Number Theory 87 (2001), no. 2, 253-269

Mathematics

Number Theory

18 pages, latex2e with amsfonts. Final version, accepted for publication

Scientific paper

10.1006/jnth.2000.2616

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.

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