An adelic causality problem related to abelian L-functions

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

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Cited by in corpus (8)

• H = x p with interaction and the Riemann zeros
• On Fourier and Zeta(s)
• A lower bound in an approximation problem involving the zeros of the Riemann zeta function
• Sur certains espaces de Hilbert de fonctions entieres, lies a la transformation de Fourier et aux fonctions L de Dirichlet et de Riemann
• The Lerch zeta function IV. Hecke operators
• A note on Nyman's equivalent formulation of the Riemann Hypothesis
• On an analytic estimate in the theory of the Riemann Zeta function and a Theorem of Baez-Duarte
• Quaternionic Gamma functions and their logarithmic derivatives as spectral functions