The Scattering Matrix for the Hilbert Modular Group
نویسنده
چکیده
In this paper, we compute the scattering matrix for the Hilbert modular group over any number field K. We then express the determinant of the scattering matrix as a ratio of completed Dedekind zeta functions associated to the Hilbert class field of K. This generalizes work of Efrat and Sarnak [ES] in the imaginary quadratic case.
منابع مشابه
On duality of modular G-Riesz bases and G-Riesz bases in Hilbert C*-modules
In this paper, we investigate duality of modular g-Riesz bases and g-Riesz bases in Hilbert C*-modules. First we give some characterization of g-Riesz bases in Hilbert C*-modules, by using properties of operator theory. Next, we characterize the duals of a given g-Riesz basis in Hilbert C*-module. In addition, we obtain sufficient and necessary condition for a dual of a g-Riesz basis to be agai...
متن کاملDilations, models, scattering and spectral problems of 1D discrete Hamiltonian systems
In this paper, the maximal dissipative extensions of a symmetric singular 1D discrete Hamiltonian operator with maximal deficiency indices (2,2) (in limit-circle cases at ±∞) and acting in the Hilbert space ℓ_{Ω}²(Z;C²) (Z:={0,±1,±2,...}) are considered. We consider two classes dissipative operators with separated boundary conditions both at -∞ and ∞. For each of these cases we establish a self...
متن کاملWigner Representation Theory of the Poincaré Group, Localization , Statistics and the S-Matrix
It has been known that the Wigner representation theory for positive energy orbits permits a useful localization concept in terms of certain lattices of real subspaces of the complex Hilbert -space. This ”modular localization” is not only useful in order to construct interactionfree nets of local algebras without using non-unique ”free field coordinates”, but also permits the study of propertie...
متن کاملProducts Of EP Operators On Hilbert C*-Modules
In this paper, the special attention is given to the product of two modular operators, and when at least one of them is EP, some interesting results is made, so the equivalent conditions are presented that imply the product of operators is EP. Also, some conditions are provided, for which the reverse order law is hold. Furthermore, it is proved that $P(RPQ)$ is idempotent, if $RPQ$†</...
متن کاملep - t h / 96 08 09 2 v 3 2 5 M ar 1 99 7 Wigner Representation Theory of the Poincaré Group , Localization , Statistics and the S - Matrix Bert Schroer Freie
It has been known that the Wigner representation theory for positive energy orbits permits a useful localization concept in terms of certain lattices of real subspaces of the complex Hilbert -space. This ”modular localization” is not only useful in order to construct interactionfree nets of local algebras without using non-unique ”free field coordinates”, but also permits the study of propertie...
متن کامل