Geometric & Functional Analysis GAFA

, Volume 9, Issue 6, pp 1128–1155 | Cite as

A Spectral Correspondence for Maaß Waveforms

  • J. Bolte
  • S. Johansson


Let \( {\cal O}^1 \) be a (cocompact) Fuchsian group, given as the group of units of norm one in a maximal order \( {\cal O} \) in an indefinite quaternion division algebra over \( {\Bbb Q} \). Using the (classical) Selberg trace formula, we show that the eigenvalues of the automorphic Laplacian for \( {\cal O}^1 \) and their multiplicities coincide with the eigenvalues and multiplicities of the Laplacian defined on the Maaß newforms for the Hecke congruence group \( \Gamma_0(d) \), when d is the discriminant of the maximal order \( {\cal O} \). We also show the equality of the traces of certain Hecke operators defined on the Laplace eigenspaces for \( {\cal O}^1 \) and the newforms of level d, respectively.


Division Algebra Trace Formula Maximal Order Fuchsian Group Congruence Group 
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Copyright information

© Birkhäuser Verlag, Basel 1999

Authors and Affiliations

  • J. Bolte
    • 1
  • S. Johansson
    • 2
  1. 1.Abteilung Theoretische Physik, Universität Ulm, Albert-Einstein-Allee 11, D-89069 Ulm, Germany, e-mail: bol@physik.uni-ulm.deDE
  2. 2.Department of Mathematics, Chalmers University of Technology and Göteborg University, S-412 96 Göteborg, Sweden, e-mail: sj@math.chalmers.seSE

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