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On Eigenfunctions of the Laplacian for Hecke Triangle Groups

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Emerging Applications of Number Theory

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 109))

Abstract

Because of their intimate connection with Schrödinger’s equation, it is not too surprising that the accurate calculation of square-integrable eigenfunctions of the Laplacian on negatively curved Riemannian manifolds, particularly in the high-energy limit, should have emerged as a topic of major interest within quantum chaos. The determination of such eigenfunctions is, after all, tantamount to examining individual quantum-mechanical “particles” on the given Riemannian manifold R — a pursuit of some importance given the classical chaos which prevails on R due to R’s curvature being negative.1

Research partially supported by the NSF.

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Author information

Authors and Affiliations

  1. School of Mathematics, University of Minnesota, Minneapolis, MN, 55455-0488, USA

    Dennis A. Hejhal

  2. Department of Mathematics, Uppsala University, Box 480, S-75106, Uppsala, Sweden

    Dennis A. Hejhal

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  1. Dennis A. Hejhal
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Editors and Affiliations

  1. School of Mathematics, University of Minnesota, Minneapolis, MN, 55455, USA

    Dennis A. Hejhal

  2. Department of Mathematics, University of British Columbia, Vancouver, British Columbia, V6T 1Z2, Canada

    Joel Friedman

  3. IBM Thomas J. Watson Research Center, Yorktown Heights, NY, 10598, USA

    Martin C. Gutzwiller

  4. AT&T Labs—Research, Florham Park, NJ, 07932-0971, USA

    Andrew M. Odlyzko

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Hejhal, D.A. (1999). On Eigenfunctions of the Laplacian for Hecke Triangle Groups. In: Hejhal, D.A., Friedman, J., Gutzwiller, M.C., Odlyzko, A.M. (eds) Emerging Applications of Number Theory. The IMA Volumes in Mathematics and its Applications, vol 109. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1544-8_11

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  • DOI: https://doi.org/10.1007/978-1-4612-1544-8_11

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7186-4

  • Online ISBN: 978-1-4612-1544-8

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