An Adelic Causality Problem Related to Abelian L–functions
نویسنده
چکیده
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. Université de NiceSophia Antipolis Laboratoire J.-A. Dieudonné Parc Valrose F-06108 Nice Cédex 02 France [email protected]
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