## The scattering matrix for the Hilbert modular group

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**137**(2009), 2541-2555 Request permission

## 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.## References

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## Additional Information

**Riad Masri**- Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
- MR Author ID: 735357
- Email: masri@math.wisc.edu
- 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
- © Copyright 2009
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc.
**137**(2009), 2541-2555 - MSC (2000): Primary 11F41
- DOI: https://doi.org/10.1090/S0002-9939-09-09800-1
- MathSciNet review: 2497465