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Proceedings of the American Mathematical Society

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The scattering matrix for the Hilbert modular group


Author: Riad Masri
Journal: Proc. Amer. Math. Soc. 137 (2009), 2541-2555
MSC (2000): Primary 11F41
Published electronically: January 28, 2009
MathSciNet review: 2497465
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Abstract: In this paper, we compute the scattering matrix for the Hilbert modular group over any number field $ K$. We then compute the determinant of the scattering matrix and show it is a ratio of completed Dedekind zeta functions associated to the Hilbert class field of $ K$. This generalizes work of Efrat and Sarnak in the imaginary quadratic case.


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Additional Information

Riad Masri
Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
Email: masri@math.wisc.edu

DOI: https://doi.org/10.1090/S0002-9939-09-09800-1
Received by editor(s): July 9, 2008
Received by editor(s) in revised form: October 13, 2008
Published electronically: January 28, 2009
Communicated by: Ken Ono
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.