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The scattering matrix for the Hilbert modular group

Author(s): Riad Masri
Journal: Proc. Amer. Math. Soc. 137 (2009), 2541-2555.
MSC (2000): Primary 11F41
Posted: January 28, 2009
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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: 10.1090/S0002-9939-09-09800-1
PII: S 0002-9939(09)09800-1
Received by editor(s): July 9, 2008,
Received by editor(s) in revised form: October 13, 2008
Posted: January 28, 2009
Communicated by: Ken Ono
Copyright of article: Copyright 2009, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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