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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The scattering matrix for the Hilbert modular group
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by Riad Masri PDF
Proc. Amer. Math. Soc. 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.
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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