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An Adelic Causality Problem Related to Abelian L-Functions

✍ Scribed by Jean-François Burnol

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 167 KB
Volume: 87
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.2000.2616

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✦ Synopsis

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.

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