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Abstrakty
We study the infinitesimal generator of the Lax-Phillips semigroup of the automorphic scattering system defined on the Poincaré upper half-plane for SL₂(ℤ). We show that its spectrum consists only of the poles of the resolvent of the generator, and coincides with the poles of the scattering matrix, counted with multiplicities. Using this we construct an operator whose eigenvalues, counted with algebraic multiplicities (i.e. dimensions of generalized eigenspaces), are precisely the non-trivial zeros of the Riemann zeta function. We give an operator model on L²(ℝ) of this generator as explicit as possible. We obtain a condition equivalent to the Riemann hypothesis in terms of cyclic vectors for a weak resolvent of the scattering matrix.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
99-122
Opis fizyczny
Daty
wydano
2007
Twórcy
autor
- Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland
Bibliografia
Typ dokumentu
Bibliografia
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DOI
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-ap92-2-1